Grade 8 Physics

IL FOUNDATION SERIES

PHYSICS

A Reliable Companion for JEE | NEET | Olympiads

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ISBN 978-81-985385-9-8 Second Edition

Contents 1.

Force and Pressure

01

2. Friction

39

3. Sound

57

4. Chemical Effects of Electric Current

81

5. Some Natural Phenomena

99

6. Light

116

1

FORCE AND PRESSURE

1.1 FORCE - A PUSH OR PULL 1.1.1 Definition of force A push or pull on a body is called force.

Push

Pull Fig. 1.1 Push or Pull

To understand this, let’s take an example: imagine you are going for a school picnic. The bus has some trouble with its battery. The driver asks the boys to push the bus. What do the boys do? They apply force during pushing so that the bus starts.

Let’s take another example: Imagine that the door of your house is jammed, as it often happens in the rainy season. Your mother tries to pull it so that it opens. However, the door does not open. She calls you for help. Both of you apply force to pull the door.

If you carefully study the above examples, you will notice that word force is associated with either pull or push, which causes some kind of motion.

•

A force cannot be seen. A force can be judged only by its effects.

•

Effect of force depends not only on the magnitude of force but also on the area on which it is applied. An interaction of one object results in a force between the two objects.

•

The strength of force is usually expressed by its magnitude.

•

Force has both magnitude and direction. If the magnitude or the direction changes, the effect of force can change.

•

The SI unit of force is newton (commonly represented as 'N’).

1

FORCE AND PRESSURE

1.2 EXPLORING FORCES 1.2.1 Magnitude and direction of a force The magnitude of a force determines its strength relative to another force. Defining a force comprehensively involves specifying both its magnitude and the direction in which it acts on the object. Changes in either the direction or magnitude of an applied force lead to corresponding alterations in its effect on the object. Understanding the interplay between magnitude and direction is crucial for comprehending the dynamics of forces in various physical scenarios.

1.2.2 Forces acting in the same direction When forces are applied to an object in the same direction, their magnitudes combine (Fig. 1.2). In such cases, the net force experienced by the object is equal to the sum of the individual forces. This additive effect results in a stronger force compared to each force acting alone.

A

F1

F2

Fig. 1.2 Forces acting in the same direction

Example: Two forces, F1 and F2, act on an object in the same direction. F1 has a magnitude of 30 newton, and F2 has a magnitude of 45 newton. Calculate the resultant force on the object when both forces are applied.

Solution: Given forces: F1 = 30 N F2 = 45 N When forces act in the same direction, the resultant force (R) can be found by simply adding the magnitudes of the individual forces: R = F1+ F2 Substitute the given values: R = 30 N + 45 N R = 75 N Therefore, the resultant force (R) when F1 and F2 act in the same direction is 75 newton.

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IL Foundation Series Class 8

1.2.3 Forces acting in opposite directions When two forces act in opposite directions on an object, the net force is determined by the difference between the two forces. The resultant force acts in the direction of the force with the higher magnitude.

For example, Fig. 1.3 shows two forces acting in opposite directions F2 B

F1 Fig. 1.3 Forces acting in opposite directions

Note: In scenarios where opposing forces are equal in magnitude, the net force is zero, resulting in no motion. However, if unequal forces are applied, the object moves in the direction of the greater force. An analogous situation occurs in a tug of war, where teams pull the rope in opposite directions, and victory is achieved by the team applying the greater force.

Example: Two forces, F1 and F2, act on an object in opposite directions. F1 has a magnitude of 80 newton, and F2 has a magnitude of 50 newton. Calculate the resultant force on the object when both forces are applied.

Solution: Given forces: F1 = 80 N F2 = 50 N When forces act in opposite directions, the resultant force R can be found by taking the difference between the magnitudes of the individual forces and the direction of the larger force determines the direction of the resultant force.

R = F1- F2 Substitute the given values: R = 80 N - 50 N R = 30 N Therefore, the resultant force (R) when F1 and F2 act in the opposite direction is 30 newton.

3

FORCE AND PRESSURE

1.2.4 Balanced and unbalanced forces •

If the resultant of all forces acting on a body is zero, the forces acting on the body are called balanced forces.

•

If the resultant of all forces acting on a body is not zero, the forces acting on the body are called unbalanced forces.

1.3 EFFECTS OF FORCES 1.3.1 A force can change the state of motion When an external force is applied to a stationary object or an object at rest, it can cause movement of that object in the direction of the applied force.

For example, when we hit a football (initially at rest), the ball continues its motion in the direction of applied force for some time until hitting an obstacle.

Or When force is applied to a moving object in the opposite direction to its motion, then the object will stop its motion.

For example, in a football game, if a goalkeeper catches the football coming towards him, he applies external force to stop it.

1.3.2 A force can change the speed of the object If an external force is applied to a moving object, it can cause a change in its speed; that is, it will either slow down or move faster depending on the type of force.

For example, the speed of a moving car decreases when the driver applies brakes.

1.3.3 A force can change the direction of the object When an external force is applied to a moving object, it can cause a change in the direction of the object.

For example, in a football game, a player changes the direction of the football by kicking it towards another player.

1.3.4 A force can change the shape or size of the object When the external force is applied to an object from multiple directions, then these multiple forces can cause a change in the shape or size of that object. Such changes may be temporary or permanent.

For example, if we squeeze a rubber ball, we are applying force from multiple directions on the ball which causes a change in the shape and size of the ball.

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IL Foundation Series Class 8

1.4 CONTACT FORCES 1.4.1 Contact force Force which results when there is a direct physical contact between two interacting objects is known as contact force.

Examples: Muscular force, frictional force, normal force, and tension etc.

1.4.2 Different types of contact forces I. Muscular force: The forces that are exerted by using body muscles are known as muscular forces. Muscles refer to multiple bundles of muscle cells held together.

Muscles are normally arranged in such a way that as one group of muscles contract, another group relaxes or lengthens.

Fig. 1.4 Muscular force

II. Force of friction: Friction is the resistance to the movement of a body over the surface of another body. The direction of friction is always opposite to the direction of motion relative to the surface of contact.

It is not possible to drive a car if there is no friction between the tyres of the car and the road. We cannot walk on a road without friction.

Ff

FA

Fig. 1.5 Frictional force

5

FORCE AND PRESSURE

III. Normal force: The direction which is perpendicular to the plane of a contact surface is said to be normal.

The force that a solid surface exerts on any object which is in contact with it in the normal direction is called the normal force.

N

mg Fig. 1.6 Normal force

IV. Tension: Tension is a contact force that always pulls the objects along a string. It is observed in strings, rubber chords and springs.

Tension in a string has a limiting value. A string or rope can exert certain a maximum pull; after this, the string or rope will get cut.

T

mg Fig. 1.7 Tension force

1.5 NON-CONTACT FORCES 1.5.1 Non-contact force (forces acting at a distance or field forces) The force that acts between two bodies when the bodies are not directly touching each other is called force at a distance, or non-contact force, or field force.

Examples: Gravitational force, magnetic force, electrostatic force.

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IL Foundation Series Class 8

1.5.2 Different types of non-contact forces I. Magnetic force: A magnet can attract or repel another magnet without contact with that magnet. This action of push or pull is referred to as magnetic force. When two magnets are brought closer, we observe that like poles repel each other and unlike poles attract each other.

Paper clips get attracted to the two ends of a horseshoe magnet due to magnetic force.

Like poles repel Unlike poles attract S

N

N

S

N

S

S

N

S

N

S

N

N

S

N

S Fig. 1.8 Magnetic force

II. Electrostatic force: The force exerted by a charged body on another charged or uncharged body is known as electrostatic force. This force comes into play even when the bodies are not in contact so it is called non-contact force or force at a distance or field force. There are two types of charges in nature: positive charge and negative charge.

Like charges repel each other and unlike charges attract each other. For example, Paper pieces will get attracted to a balloon if we rub the balloon with our hair or something which is uncharged. This happens because the balloon will get electrically charged.

Like charges repel

{ --

Opposite charges attract

+

+

+

-

Fig. 1.9 Electrostatic force

III. Gravitational force: A force of attraction that exists between any two bodies (or masses) everywhere in the universe is called gravitational force. An apple falls from a tree because of gravitational attraction between the earth and the apple.

7

FORCE AND PRESSURE

Earth Moon Gravitational force of the moon

High tide

High tide Fig. 1.10 Gravitational force

1.6 FREE BODY DIAGRAM 1.6.1 Equilibrium of forces Objects experience a state of equilibrium when the sum of forces acting on them is zero. This equilibrium holds true for both stationary objects and objects moving at a constant velocity.

Mathematically, Fnet = 0.

1.6.2 Free body diagram A free body diagram (FBD) consists of a diagrammatic representation of a single body or a subsystem of bodies isolated from its surroundings showing all the forces acting on it.

Points to remember: 1. Newton's First Law: An object remains at rest or in uniform motion unless acted upon by an external force.

2. Newton's Second Law: The Force on an object is given by F = ma.

3. Newton's Third Law: For every action, there is an equal and opposite reaction.

Working with Newton's First and Second Law

Step 1: Reference frame: Check whether the reference frame is inertial or non-inertial.

F A

B

Fig. 1.11

Step 2: Decide the system: Decide the system on which the laws of motion are to be applied. The system may be a single particle, a block, a combination of two blocks one kept over the other, two blocks connected by a string, a piece of string etc.

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IL Foundation Series Class 8

System F

a.

A

(or)

B System

F

b.

A

(or)

B System

F

c.

A

B

Fig. 1.12

The only restriction is that all parts of the system should have the same acceleration.

Step 3: Identify the external contacts and forces: Once the system is decided make a list of the forces acting on the system due to all the objects other than the system. Any force applied by the system should not be included in the list of forces.

NA F

N1

A f

mg Fig 1.13

Step 4: Choose a coordinate system and draw an acceleration diagram. When the forces are coplanar, only two axes, say X and Y, taken in the plane of forces are needed.

Choose the X-axis along the direction in which the system is known to have or is likely to have the acceleration. A direction perpendicular to it may be chosen as the Y-axis. If the system is in equilibrium, then any mutually perpendicular directions in the plane of the diagram may be chosen as the axis.

NA F

y N1

A f

a

mg

ay ax

x

Fig. 1.14

Step 5: Application of F = ma: Write the components of all the forces along the x-axis and equate their sum to the product of the mass of the system and its acceleration. This gives us one equation.

9

FORCE AND PRESSURE

Write the components of forces along y-axis and equate their sum to zero. This gives us another equation. These are called equations of motion. Solve the equations to get the unknown quantities.

Fx max Fy may ∑Fx ≠ 0 when the system is in vertical equilibrium ay = 0, ax ≠ 0 ∑Fy ≠ 0 when the system is in horizontal equilibrium ay ≠ 0, ax= 0 Example: Consider the situation shown in the following figure. The boy stands on the floor in a room on the earth balancing a heavy load of mass 'm' on his head. Find the force applied by the boy on the load.

Fig. 1.15

Solution: Step 1: The boy is in a room on the earth. If we consider the room as a reference frame, it is an inertial frame.

Step 2: Now we decide the load as a system.

Step 3: Now we list out the forces acting on the system.

System Load

Force exerted by

Magnitude of the force

Direction of the force

Nature of the force

Earth

W

Downward

Gravitational

Boy

N

Upward

Electromagnetic force

Step 4: N

O

(here ’O’ is origin)

W

Fig 1.16

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IL Foundation Series Class 8

Step 5: Application of F = ma along x-axis no forces are there along x-axis. So ma=0  a=0 The components of the forces along y-axis are N in the upward direction and w = mg in the downward direction.

Sign convention: If we consider downward direction as positive, then upward direction is negative. w-N=0 N=w Therefore, N = mg Connected bodies

Case (i): m1

T1

T1

m2

T2

T2

m3

F

Fig. 1.17 Connected bodies

Three bodies of masses m1, m2, m3 are connected by strings, as shown in the figure (Fig. 1.17). The bodies are lying on a frictionless horizontal surface. A force F is applied as shown. All the bodies move with the same acceleration 'a'.

F = ( m1 + m2 + m3 ) a a=

F ...(1) m1 + m2 + m3

Let T1 be the tension in the string between blocks m1 and m2. a T1 m1 Fig. 1.18

F = ( m1 + m2 + m3 ) a F a= m1 + m2 + m3 Let T2 be the tension in the string connected between the blocks m2 and m3.

11

FORCE AND PRESSURE

a

m2

T1

T2

Fig.1.19

T2-T1 = m2a T2=T1 + m2a T2=m1a + m2a T2=(m1+ m2)a =

(m1+ m2)F m1+ m2+ m3

Case (ii): Pulley (Atwood's Machine): The atwood machine is used to determine acceleration due to gravity at a place. The simple Atwood machine consists of two masses 'm1' and 'm2' connected by a light string passing over a smooth, frictionless pulley, fixed to the ceiling. When the system is released, both the masses move with the same acceleration say 'a'. As the pulley is smooth the tension of string is same on either side of the pulley.

Let m1 be greater than m2.

The mass m1 moves down and m2 moves up with same acceleration a. Free body diagram of m1.

T T

T

a m1

m2 m g 1

Fig. 1.20 Pulley

The forces acting on m1 are (1) its weight m1g acting down and (2) The tension T acting upward ∴ m1g - T = m1a .....(1) Free body body diagram of m2 is

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IL Foundation Series Class 8

T

a

m 2g Fig. 1.21

The forces acting on m2 are (1) its weight acting downward and (2) the tension T acting upward ∴ T-m2g = m2a .....(2) Adding (1) & (2), m1g - m2g = (m1+m2 )a ∴ acceleration, a=

(m1 − m 2 ) g m1 − m 2 ....(3)

Substituting the value of 'a' in equation (1) m1g − T = m1

( m1 − m2 ) g m1 + m2

= T m1g − m1g

( m1 − m2 ) m1 + m2

 ( m + m2 ) − ( m1 − m2 )  = m1g  1  m1 + m2    2m1m2  = ∴T   g …(4)  m1 + m2  Example: A body m1 of mass 10kg is placed on a smooth horizontal table. It is connected to a string which passes over a frictionless pulley and carries at the other end, a body m2 of mass 5kg. What acceleration will be produced in the bodies when the nail fixed on the table is removed? What will be the tension in the string during the motion of the bodies? What is the tension in the string when the bodies stop? (Take g = 9.8 Nkg-1) Solution: When the nail fixed on the table is removed, the system of two bodies moves with an acceleration a in the direction as shown.

13

FORCE AND PRESSURE

R a

m1

T

m1g

a

m2 m2g Fig 1.22

From Newton's second law, we have

m1 m 2 a m 2 g a

m2g 5 9.0

3.27 ms 2 m1 m 2 10 5

Also, T = m1 × a = 10 × 3.27 N = 32.7 N When the bodies stop, acceleration, a = 0. Suppose the tension in the string becomes T'. As the net force on each body is zero, so for body m2, we can write T '= m 2 g = 5 × 9.8 = 49 N.

1.7 PRESSURE AND THRUST 1.7.1 Thrust A force acting normally on a surface is called thrust.

14

•

Its unit in CGS system is dyne.

•

Its unit in SI system is newton (N).

•

The gravitational unit of thrust is kilogram force (kgf).

•

Its Dimensional formula is [M1 L1 T-2].

•

It is a vector quantity.

IL Foundation Series Class 8

1.7.2 Pressure The force (thrust) acting normally on unit surface area is called pressure. If a thrust F acts on an area A such that P is the pressure, then mathematically, Pressure (P) =

Thrust Area

•

Pressure unit in CGS system is dyne/ cm2.

•

Its unit in SI system is N/m2 or pascal (Pa).

•

Its dimensional formula is [M1 L-1 T-2].

•

It is a scalar quantity.

•

Nm-2 is also called pascal (Pa) in honour of physicist Pascal who discovered the law for the transmission of pressure in fluids.

Pascal: When a force of 1N (thrust) acts normally on an area of 1 m2, then pressure acting on the surface is called 1 pascal.

SOLVED EXAMPLES Example 1: Calculate the pressure produced by a force of 1000 N acting on an area of 2.0 m2.

Solution: Force = 1000 N Area = 2m2 Pressure = ?

The formula of pressure is given by: Force Area 1000N Pressure 500N / m 2 2 2m Pressure

Therefore, the pressure exerted on the given area will be 500 N/m2.

Example 2: A vessel of 200 cm2 cross sectional area contains water. The mass of water is 4 kg. Find the pressure acting on the bottom surface.

Solution: Mass of water in the vessel = 4 kg ∴Weight = mg = 4 kg × 9.8 m s-2 = 39.2 N. Area of the bottom surface = 200 cm2 = 2×10-2 m2 15

FORCE AND PRESSURE

∴ Pressure =

Thrust(Weight) = Area

39.2 N = 1960 N m -2= 1960 Pa 2 x 10 -2 m 2

Example 3: A cuboid has dimensions as shown. If the mass of the block is 5 kg, find the minimum and maximum pressure it exerts as the orientation of the body is changed.

10 cm

5 cm 20 cm Fig 1.23

Solution: The weight exerted by the block = mg = 5 kg × 9.8 ms-2 = 49 N For the pressure to be minimum, this weight should act on maximum area and the block should be placed with the largest lateral surface on the bottom side.

Pmin =

49 N = 2450 N m -2 -4 10 × 20 × 10

For pressure to be maximum, the area on which the weight of the block acts, should be minimum and the block should be placed with the smallest lateral surface as the bottom side.

Pmax =

49 N = 9800 N m -2 −4 5 × 10 × 10

1.7.3 Density Density refers to the mass per unit volume of a substance.

Mathematically, density ( ρ ) is calculated using the formula:

ρ = m/V Where, ρ is the density, m is the mass of the object, and V is the volume of the object.

1.8 PRESSURE EXERTED BY LIQUIDS AND GASES 1.8.1 Pressure in a fluid When a fluid (either liquid or gas) is at rest, it exerts a force perpendicular to any surface in contact with it, such as a container wall or a body immersed in the fluid.

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IL Foundation Series Class 8

While the fluid as a whole is at rest, the molecules that make up the fluid are in motion, the force exerted by the fluid is due to molecules colliding with their surroundings.

If we think of an imaginary surface within the fluid, the fluid on the two sides of the surface exerts equal and opposite forces on the surface, otherwise the surface would accelerate and fluid would not remain at rest. dF dA

dF

Fig 1.24 Pressure in a fluid

Consider a small surface of area dA centred on a point on the fluid. The normal force exerted by the fluid on each side is dF⊥ . The pressure P is defined at that point as the normal force per unit area, i.e., P = ( dF⊥ )/dA If the pressure is the same at all points of a finite plane surface with area A, then P = F⊥ /dA Where F⊥ is the normal force on one side of the surface.

1.8.2 Pascal's law 'The pressure in a fluid in equilibrium is same everywhere if the effect of gravity can be neglected'.

It was formulated by Blaise Pascal. This law constitutes one of the basic Principles of hydrostatics.

Mathematical Expression for pressure in fluids with pressure of gravity

Consider a liquid of density ' ρ ' contained in a beaker. Consider a liquid column of height 'h' and area of cross-section 'a'. Let A and B be the top and bottom surfaces of the liquid column.

A

a

Beaker h

Liquid

B Fig. 1.25

17

FORCE AND PRESSURE

∴ Volume of liquid column (V) = area of cross section × length = ah Mass of liquid column = volume × density Mass of liquid column = V × ρ Mass of liquid column = ah ρ ∴ Weight of liquid column = mass × acceleration due to gravity = mg = ah ρ g ∴ Thrust exerted by the liquid column on the base of the beaker = ah ρ g ∴ Pressure due to liquid column: Thrust a gh

Area a So, P h g P

∴ Pressure (P) = liquid columns' height (h) × liquid density ( ρ ) × acceleration due to gravity (g) Factors on which the pressure at a point in fluids depends

•

Pressure in a fluid is directly proportional to its height (or) depth.

•

Pressure in a fluid is directly proportional to its density.

•

Pressure in a fluid is directly proportional to acceleration due to gravity.

•

Pressure in a fluid is independent of the area of cross-section.

•

If PA is pressure due to atmosphere then total pressure at point B is PB = PA + h ρ g.

Laws of liquid pressure

•

Pressure at a point inside the liquid increases with the depth from the free surface of the liquid.

•

Pressure at a point inside liquid at a given depth increases with increase in the density of the liquid.

•

Pressure is same in all directions, about a given point within the liquid.

•

Pressure is same at all points in a horizontal plane at a given depth in stationary liquid.

•

A liquid seeks its own level.

SOLVED EXAMPLES Example 1: A submarine is cruising at a depth of 1000 m below sea level. The density of seawater is 1025 kg cubic meters. What is the pressure exerted by the seawater on the submarine?

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IL Foundation Series Class 8

Solution: Density of the seawater = 1025 kg/m3, Depth of the seawater = 1000 m, Acceleration due to gravity = 10 m/s2.

So, the pressure exerted by the seawater on the submarine is: Pressure = Density × Depth × Acceleration due to gravity =1025 kg/m3 × 1000 m × 10 m/s2 = 1,02,50,000 Pa Therefore, the pressure exerted by the seawater on the submarine is 1,02,50,000 Pa. Example 2: A dam is filled with water till a height of 127 meters. If the mass of water per cubic centimetre is one gram, then find the difference in pressures acting at the following two points. (a) Point exactly at a depth half that of the dam. (b) Point at the bottom of the dam.

Solution: Height/depth of dam =127 metres.

Density ( ρ ) = Mass /Volume = 1gram/(1 cm3 ) = 1 gcm-3 = 1000 kg m-3 Height of the point = depth/2 = 127/2 = 63.5m Pressure at a point (Pa ) = h ρ g = 63.5 × 103 × 10 = 635 × 103 pascals Depth of the point =127 m Pressure at a point (Pb ) = 127 × 103 × 10 = 1270 × 103 pascals.

Therefore, Difference in pressures = Pb-Pa = (1270-635) × 103 = 635 × 103 Pa 1.8.3 Buoyancy and Archimedes’ principle Buoyancy: Consider a part ABCD of the fluid. Let the mass of the part of the fluid be (mf). When the part of the fluid ABCD is at rest: B

A

B

D

C mfg Fig. 1.26 Buoyancy

19

FORCE AND PRESSURE

The weight of ABCD(mf g) is balanced by an upward force exerted by the remaining fluid. This upward force exerted by the remaining fluid is called Buoyant force (B).

B = mf g ⇒ B = Vρ f g Where V is the volume of the fluid displaced and ρf is the density of the fluid.

Note: If the part of the fluid is replaced by another object of same volume irrespective of material, buoyant force remains same when the fluid is at rest.

B

m0 is the mass of the object m0g Fig. 1.27 Buoyant force

Therefore, Buoyant Force = weight of fluid displaced This phenomenon is known as Buoyancy.

Archimedes' principle: When a body is partially or fully dipped into a fluid at rest, the fluid exerts an upward force of buoyancy equal to the weight of displaced fluid.

1.8.4 Atmospheric pressure (P0) It is the pressure of the earth's atmosphere. This changes with weather and elevation. Normal atmospheric pressure at sea level is 1.013×105 Pa. 1 atm = 1.013×105 Pa Activity

Let's do an activity to understand the effect of atmospheric pressure. Empty a can and fill it with water. Set the can on a tripod stand and apply heat using a burner. Once the water reaches a boiling point, steam will emerge, displacing the air inside the can. Keep heating until steam escapes freely from the can's mouth. Cease heating and promptly seal the can tightly. Detach the can from the tripod stand and cool it by pouring cold water. The observation reveals that the can collapses due to the atmospheric pressure exerted on it.

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IL Foundation Series Class 8

Steam pressure Air pressure Water

Fig. 1.28 Demonstration of atmospheric pressure When cold water is applied to the can, the steam within condenses back into water, leading to a significant decrease in pressure. Simultaneously, the external atmospheric pressure, being substantial, presses upon the can, causing it to collapse.

At sea level, atmospheric pressure is commonly measured in atmospheres (atm). The standard atmospheric pressure at sea level is 1 atm.

Experimental findings indicate that at sea level, a mercury column of approximately 76 cm exerts an equivalent pressure to that of the atmospheric air.

The relationship between pressure (P), height of the mercury column (h), and the density of mercury ( ρ ) is represented by the equation P = h ρ g.

Where h= height of mercury column =76 cm of Hg = 0.76 m of Hg d density of mercury 13.6gm 3 (or) 13.6 103 kgm 3 g 9.8ms 2 1 atm 0.76 13.6 103 9.8 Pa 1.013 105 Pa ~ 105 Pa. Different units of pressure

1Pa = 1Nm −2 1kg f m −2 = 9 ⋅ 8Pa 105 dyne 1Nm = 104 cm2 1Pa = 10 dyne cm −2 −2

1bar ≈ 105 Pa 1 torr = 1 mm of Hg 1 atm ≅ 1.013 bar

21

FORCE AND PRESSURE

QUICK REVIEW

22

•

A push or pull on a body is called force.

•

When forces are applied to an object in the same direction, their magnitudes combine.

•

When two forces act in opposite directions on an object, the net force is determined by the difference between the two forces.

•

If the resultant of all forces acting on a body is zero, the forces acting on the body are called balanced forces.

•

If the resultant of all forces acting on a body is not zero, the forces acting on the body are called unbalanced forces.

•

A Force can change the state of motion, speed, direction, and shape of the object.

•

Force which results when there is direct physical contact between two interacting objects is known as contact force.

•

Different types of contact forces: Muscular force, frictional force, normal force, tension etc.

•

The force which acts between two bodies when the bodies are not directly touching each other is called non-contact force.

•

Different types of non-contact forces: Gravitational force, magnetic force, electrostatic force.

•

Objects experience a state of equilibrium when the sum of forces acting on them is zero.

•

A free body diagram (FBD) consists of a diagrammatic representation of a single body or a sub-system of bodies isolated from its surroundings showing all the forces acting on it.

•

A force acting normally on a surface is called thrust.

•

The force (thrust) acting normally on unit surface area is called pressure, i.e., P = F/A

•

Density refers to the mass per unit volume of a substance.

•

When a fluid (either liquid or gas) is at rest, it exerts a force perpendicular to any surface in contact with it, such as a container wall or a body immersed in the fluid.

•

Pascal's law: The pressure in a fluid in equilibrium is same everywhere if the effect of gravity can be neglected.

•

P = hρ g

•

Buoyant Force = weight of fluid displaced, and this phenomenon is known as Buoyancy.

•

Archimedes' principle: When a body is partially or fully dipped into a fluid at rest, the fluid exerts an upward force of buoyancy equal to the weight of displaced fluid.

•

Atmospheric pressure: It is pressure of the earth's atmosphere. This changes with weather and elevation. Normal atmospheric pressure at sea level is 1.013×105 Pa or 1 bar.

IL Foundation Series Class 8

WORKSHEET - 1 MULTIPLE CHOICE QUESTIONS WITH SINGLE CORRECT ANSWER I. Force - a push or pull; and exploring forces

1. Which of the following is the SI unit of force? a. dyne

b. gram-weight

c. newton

d. joule

2. In below figure, two boys A and B are shown applying force on a block. If the block moves towards the right, which one of the following statements is correct?

A.

B.

a. Magnitude of force applied by A is greater than that of B. b. Magnitude of force applied by A is smaller than that of B. c. Net force on the block is towards A. d. Magnitude of force applied by A is equal to that of B. 3. To draw water from the well, we should __________ the rope. a. pull

b. push

c. kick

d. lift

4. When the two forces act in the same direction, the magnitude of the net force is a. Product of the two forces

b. Equal to the difference of the magnitudes of the individual forces

c. Equal to the sum of the magnitudes of

d. None

the individual forces 5. Let the force F1 and F2 act on the table in opposite directions, the net force is a. F1− F2

b. F1 + F2

c. 0

d. 2F1 - F2

6. Which of the following pairs of forces will never give a resultant force of 2N? a. 2N and 2N

b. 1N and 1N

c. 1N and 3N

d. 3N and 5N

II. Effects of forces, contact and non-contact forces

1. Which of the statements is correct about force?

A) Force can change the state of an object B) Force can change the direction of an object C) Force can change the speed of an object a. B only

b. A, B and C

c. B and C only

d. C only 23

FORCE AND PRESSURE

2. When a batsman hits the ball for a boundary, he a. changes only the speed of the ball

b. changes the speed and direction of the ball

c. changes only the direction of the ball.

d. does not change the direction and speed of the ball.

3. Which of the following are examples of situations in which applied force causes a change in the shape of an object? a. Pushing a car that is parked with brakes engaged

b. Pushing a wall with your hand

c. Squeezing a sponge

d. None

4. In the circuit shown in below figure, when the circuit is completed, the hammer strikes the gong. Which of the following forces is responsible for the movement of the hammer?

a. Gravitational force alone

b. Magnetic force alone

c. Electrostatic force alone

d. Frictional force alone

5. During dry weather, while combing hair, sometimes we experience hair flying apart. The force responsible for this is a. force of gravity

b. force of friction

c. electrostatic force

d. magnetic force

6. Which one of the following forces is a contact force? a. force of gravity

b. magnetic force

c. force of friction

d. electrostatic force

7. Which of the following actions is involved when a magnet attracts a piece of iron toward it? a. Pushing

b. Pulling

c. Flying

d. Picking

8. What is a muscular force?

24

a. The force resulting due to the action of muscles

b. A frictional force

c. The force due to a magnet

d. The force generated by an electric current in a wire

IL Foundation Series Class 8

9. Which of the following forces is also called as force at a distance? a. Contact force

b. Non-contact force

c. Pseudo force

d. Linear force

10. What is an electrostatic force? a. The force exerted by a charged body on another charged or uncharged body. b. The force that keeps planets in orbit around the sun. c. The force that holds the protons and neutrons together within an atomic nucleus. d. The force exerted between magnetic objects or a magnetic field and a magnetic object.

III. Free body diagram

1. What will be the net force acting on the box given below?

15 N 20 N 8N

32 N 15 N

a. A net force of 28 N will be exerted in the right direction.

b. A net force of 4 N will be exerted in the left direction.

c. A net force of 90 N will be exerted in the downward direction.

d. The net force on the body will be zero.

2. In the representation of Free body diagram, if the forces are coplanar a. Only one axis say X, taken in the plane of forces it is needed. b. Only two axes, say X and Y taken in the plane of forces are needed. c. No axes are needed. d. It is difficult to say how many axes are needed.

3. In the representation of Free body diagram, the only restriction is that all parts of the system should have a. Identical acceleration

b. Different acceleration

c. Non-uniform acceleration

d. No need to consider acceleration

25

FORCE AND PRESSURE

4. Two bodies 'A' and 'B' are connected by a string over a pulley (see the fig). The distance covered by 'A' is same as the distance covered by 'B', but their directions are different. Then A

B

a. A can't be treated as a system.

b. (A + B) can't be treated as a system.

c. B can't be treated as a system.

d. A can't be treated as a system but B can be treated as a system.

5. Two bodies A and B are connected by a string over a pulley and a disc slides over the string (see the figure). Then (B + D) cannot be treated as a system. The reason is A

D

B

a. The distance covered by B and D are equal

b. The distance covered by B and D are not equal

c. The directions of B and D are the same

d. The directions of B and D are not same

6. Two 10 kg bodies are attached to a spring balance as shown in below figure. The reading of the balance will be Spring scale

10 kg

a. 20 kgwt 26

b. 10 kgwt

10 kg

c. zero

d. 5 kgwt

IL Foundation Series Class 8

IV Pressure and thrust

1. A brick is kept in three different ways on a table as shown in below figure. The pressure exerted by the brick on the table will be

A

B

C

a. Maximum in position A

b. Maximum in position C

c. Maximum in position B

d. Equal in all cases

2. Which factor affects the pressure exerted by a solid on a surface? a. The mass of the solid

b. The area of the surface in contact with the solid

c. Both A and B

d. The colour of the solid

3. Calculate the pressure produced by a force of 1000 N acting on an area of 2.0 m2. a. 2000 N/m2

b. 4000 N/m2

c. 500 N/m2

d. 1000 N/m2

4. Why are the straps of a school bag made wider? a. To decrease the gravitational force exerted on the bag.

b. To decrease the pressure exerted by the bag on the shoulder.

c. To increase the force exerted on the bag.

d. To decrease the total force exerted by the bag on the shoulder.

5. A blunt knife does not cut an apple easily because a. Thicker edges produce less pressure

b. Thicker edge will transfer no force

c. Thicker edges produce more pressure

d. The weight of the knife is small

6. The mass of a boy is 20 kg and the area of the sole of his foot is 0.01m2. If g =10 m/s2. The pressure exerted on the floor when he is standing on one foot is a. 2,000 N/m2

b. 20,000 N/m2

c. 200 N/m2

d. 2,00,000 N/m2

7. The dimension of the metallic cuboid is 30 cm × 20 cm × 15 cm and its mass is 30 kg. If g =10 m/s2 then what is the pressure exerted by the cuboid when it is resting on the face having 20 cm×15 cm on the table? a. P = 104 Pa

b. P = 106 Pa

c. P = 105 Pa

d. P = 102 Pa 27

FORCE AND PRESSURE

V. Pressure exerted by liquids and gases

1. In below figure, shows a container filled with water. Which of the following statements about the pressure of water is correct?

A B C

a. Pressure at A > Pressure at B > Pressure at C

b. Pressure at A = Pressure at B = Pressure at C

c. Pressure at A < Pressure at B > Pressure at C

d. Pressure at A < Pressure at B < Pressure at C

2. Which of the following statements are correct?

A) 760 torr is equal to 1 atmosphere B) 106 dynes/cm2 is called 1 bar C) 105 newtons/m2 is pascal D) 1 atmosphere is 1.013×105 dynes/m2 a. A, C

b. A, B

c. A, D

d. C, D

3. The water pressure on your body as you go further underwater ______. a. decreases

b. increases

c. stays the same

d. becomes zero

4. The change in the shape of a hot tin can when poured with cold water on it is because a. Pressure inside the can is less than the pressure outside

b. Pressure inside the can is more than the pressure outside

c. Pressure outside the can is same as the pressure inside

d. Pressure inside the can is equal to that at the mouth

5. A vessel contains water up to a height of 1.5 m. Taking the density of water 103 kgm-3, acceleration due to gravity 9.8 m/s2 and area of the base of the vessel 100 cm2, calculate the thrust at the base vessel. a. 161 N

28

b. 133 N

c. 147 N

d. 127 N

IL Foundation Series Class 8

6. Which law states that pressure exerted in any confined mass of fluid is transmitted undiminished in all directions? a. Newton's third law of motion

b. Archimedes principle

c. Pascal's law

d. Law of floatation

7. What will be the height of the first floor if the pressure of water on the ground floor is 4×104 Pa and 104 Pa on the first floor? (Density of water = 1000 kgm-3 and g = 10 ms-2) a. 4 m

b. 3 m

c. 5 m

d. 4.5 m

WORKSHEET - 2 MULTIPLE CHOICE QUESTIONS WITH SINGLE CORRECT ANSWER 1. N/m2 is the unit of a. Force

b. Pressure

c. Thrust

d. Weight

c. Both a & b

d. None of these

2. Gravitational force always causes a. Attraction

b. Repulsion

3. The speed of a falling body increases continuously. This is because a. No force acts on it

b. It is very light

c. The air exerts a frictional force on it

d. The earth attracts it

4. 1 kg.weight is equal to a. 9.8 dyne

b. 9.8 N

c. 980 dyne

d. 980 N

5. As altitude increases a. Pressure due to air increases

b. Density of air increases

c. Density of air decreases

d. Both pressure and density increases

6. If a body is not accelerated a. No force acts on it

b. No unbalanced force acts on it

c. The resultant force is not zero

d. A single force acts on it

7. The force of friction between two bodies is a. Parallel to the contact surface

b. Perpendicular to the contact surface

c. Inclined at 30° to the contact surface

d. Inclined at 60° to the contact surface

8. The buoyant force on a body acts in a a. Vertically downward direction

b. Vertically upward direction

c. Horizontal direction

d. Direction between the horizontal and the vertical

9. Which of the following is correct? a. Pressure in a fluid directly proportional to its density

b. Pressure in a fluid inversely proportional to its density 29

FORCE AND PRESSURE

c. Pressure in a fluid inversely proportional to height

d. Both b & c

10. The pressure exerted by the atmospheric air is known as a. atmospheric pressure

b. biosphere

c. troposphere

d. all of these

11. In an aneroid barometer, the liquid used is a. water

b. mercury

c. alcohol

d. no liquid

b. force / area

c. mass / area

d. density / area

b. pressure

c. push or pull

d. friction

12. Pressure is a. volume / area 13. Force is a. power

14. Which is not the non-contact force? a. electrostatic force

b. magnetic force

c. force due to gravity

d. muscular force

15. A common balance is used for measuring a. mass

b. weight

c. pressure

d. speed

16. Which of the following scenarios involves the effect of force and can be adequately described using classical physics principles? a. A cricket ball being hit by a bat

b. A dust particle floating in air

c. The behavior of a hydrogen atom

d. All the above

17. 1 bar is equal to a. 105 N/m2

b. 105 pa

c. 10-5 N/m2

d. both a & b

18. Choose the correct option. a. pressure is a scalar quantity

b. force is a vector quantity

c. SI unit of pressure is N/m2

d. all the above

19. Magnetic force is a. force of pull

b. force of push

c. a force at a distance

d. all the above

20. When two people push the table in opposite directions the net force a. decrease and may become zero

b. only decreases

c. may increase

d. none of these

21. When we stretch the rubber bands using our fingers, the net force exerted on fingers by the rubber bands

30

IL Foundation Series Class 8

a. increases in number

b. decreases in number

c. becomes zero

d. sometimes becomes zero

22. Example(s) where the state of motion of an object changes due to the application of force. a. A ball is moved from its position of rest

b. A moving ball is brought to rest

c. A cricket ball which is at rest is hit by a bat

d. All the above

23. Example(s) where the state of motion of object changes in direction due to application of force. a. A car travelling with a velocity of 60kmph towards the North suddenly turned towards the West, keeping its magnitude constant. b. When a body is moving in a vertical circle from the bottom to the top c. Any body which is going on any curved path d. All the above 24. When you hit a coin with the striker, a. the coin changes its direction

b. the striker changes its direction

c. both a & b

d. none of these

25. Choose the correct statement. a. If a net force acts in the direction of motion, then the speed of an object moving with constant speed also increases. b. If a net force acts in a direction opposite to the motion, then it either slows the object down or brings it to a stop. c. If a net force acts in the direction of motion, then it either slows the object down or brings it to a stop. d. Both a & b are true 26. Choose the correct statements. a. Pushing the rounded end of a pencil on the palm is different compared to pushing the sharp end. b. Porters place turbans (talapaga) on their heads when they have to carry heavy loads. c. School bags and shopping bags have broad straps as handles. Lorries carrying heavy loads have a larger number of broader tyres. d. All the above 27. When you place two rectangular bricks of equal mass and similar shape, one brick vertically and another horizontally in a tray containing lime powder or fine sand, a. You may notice that the brick standing vertically sinks deeper in lime powder than the brick standing horizontally

31

FORCE AND PRESSURE

b. The contact area on which force is acting is smaller in the case of brick standing vertically c. The pressure exerted by the brick in vertical position on lime powder is greater than the brick present in horizontal position. d. All the above 28. The sharper side of a knife cuts more easily than its blunt side because a. Sharp knife of a side has a smaller contact area b. For the same amount of force applied to it, the sharp side of knife exerts more pressure than the blunt side c. For a given force, if the surface area is smaller, the pressure will be greater. d. All the above 29. The vector quantity among the following is a. Force

b. Pressure

c. Both a & b

d. None of these

b. Direction

c. Both a & b

d. None of these

b. Direction

c. Both a & b

d. None of these

30. The vector has a. Magnitude 31. A scalar has a. Magnitude

32. When we press the bulb of a dropper with its nozzle kept in water, the air in the dropper is seen to escape in the form of bubbles. Once we release the pressure on the bulb, water gets filled in the dropper. The rise of water in the dropper is due to the a. Pressure of water

b. Gravity of the earth

c. Shape of rubber bulb

d. Atmospheric pressure

33. Consider the normal force on a book at rest on a tabletop. If the table is tilted so that the surface forms an inclined plane, then a. The magnitude of the normal force changes

b. The magnitude of the net force is not zero

c. The magnitude of net force is zero

d. Both a and b

34. Two cars of unequal masses use similar tyres. If they are moving at the same initial speed, then the minimum stopping distance

32

a. is smaller for the heavier car

b. is smaller for the lighter car

c. is the same for both cars

d. depends on the volume of the car

IL Foundation Series Class 8

35. The contact force exerted by body A on another body B is equal to the normal force between the bodies. We conclude that a. The surfaces must be frictionless

b. The force of friction between the bodies is zero

c. The magnitude of normal force equals that of friction

d. The bodies must be rough but they don't slip on each other

36. Which of the following is true in the case of contact forces? a. They do not possess field

b. They have definite magnitude at the surface of the contact.

c. They change their magnitude depending on distance and parameters

d. Both a and b

37. The tools meant for cutting always have sharp edges because a. A sharper side of a tool can cut more easily than a blunt side of it b. The sharp side of the tool has a smaller contact area c. When the same amount of force is applied to it, the sharp side of the tool exerts more pressure than the blunt side d. All the above 38. We can increase the pressure by keeping the force unchanged and a. by decreasing the magnitude of area

b. by increasing the magnitude of area

c. by changing the direction of force

d. none of these

39. When the spring balance and weight hanger system is taken and slowly pulled up then a. The reading in the spring balance increases

b. The reading in the spring balance decreases

c. The string is broken

d. None of these

40. When the spring balance and weight hanger system is taken and lifted up quickly then a. The reading in the spring balance increases

b. The reading in the spring balance decreases

c. The string is broken

d. None of these

41. A block A of mass mA is kept on an inclined surface just begins to slide at an inclination of 30°. The block is replaced by another block of a different material with mass mB and it is found that it just begins to slide if the inclination is 40°. What will be an appropriate relation between the masses? a. mA> mB

b. mA < mB

c. mA = mB

d. All three cases are possible

33

FORCE AND PRESSURE

42. When a horse pulls a cart, the force which helps the horse to move forward is a. The force exerted by the horse on the ground

b. The force exerted by the cart on the ground

c. The force exerted by the ground on the horse

d. The pulling force exerted by the horse on the cart.

43. A stone is suspended by a thread from a rigid support, and another thread of the same quality is attached at the bottom of the stone. If the lower thread is pulled suddenly, then a. the upper thread will break first

b. the lower thread will break first

c. both will break at the same time

d. none of the two threads will break

44. In a situation, the contact force by a rough horizontal surface on a body placed on it has constant magnitude. If the angle between this force and the vertical is decreased the frictional force between the surface and the body will a. increase

b. decrease

c. remain the same

d. may increase or decrease

45. While walking on ice, one should take small steps to avoid slipping. This is because smaller steps ensure a. more friction

b. lesser friction

c. larger normal force and more friction

d. smaller normal force

46. Which of the following is not true in the case of non-contact forces? a. They have definite magnitude at the point of application b. They can be represented by field lines. c. They cannot be represented by field lines or lines of force. d. All of the above 47. When you push a heavy object, it doesn't move because a. Heavier objects experience large contact force due to strong interlocking between the surfaces in contact. b. The applied force on the heavy body is balanced by the force of friction developed parallel to the surface of contact c. The net force will become zero until the applied force is greater than the contact force d. All the above 48. Which are the examples that explain change of pressure? a. Porters place turbans (talapaga) on their head when they have to carry heavy loads. b. Skis have a large area so they do not sink in the snow. c. Knives have a small area so that they can cut through objects. d. All the above 34

IL Foundation Series Class 8

49. Pressure does not have direction because a. When a force is applied from one direction on the soft particle, the soft particle gets distorted and projects out in all directions b. When a force is applied from one direction on the soft particle, the soft particle exerts the force in all directions c. When a force is applied from one direction on the soft particle, the net force it exerts on the surrounding particles will become zero d. All the above 50. The unit of thrust in the SI system is a. dyne

b. joule

c. newton

d. pascal

51. The force (thrust) acting normally on the unit surface area is called a. volume

b. density

c. mass

d. pressure

52. The unit torr is related to the barometric height as : a. 1 torr = 1 cm of Hg

b. 1 torr = 0.76 m of Hg

c. 1 torr = 1 mm of Hg

d. 1 torr = 1 m of Hg

53. 1 bar =____ Pa a. 106

b. 105

c. 107

d. 108

b. Area/Thrust

c. Thrust × Area

d. Thrust + Area

54. Pressure (P) = a. Thrust /Area

55. Consider two points A and B in the same horizontal line inside a fluid then A

B

a. Pressure at A is more than the pressure at B

b. Pressure at B is more than the pressure at A

c. Pressure at A = Pressure at B

d. Both a and b are true

56. The three vessels shown in the figure have the same base area. Equal volumes of a liquid are poured into the three vessels. The Force on the base will be

A

B

C

a. Maximum in vessel A

b. Maximum in vessel B

c. Maximum in vessel C

d. Equal in all the vessels 35

FORCE AND PRESSURE

57. Equal mass of three liquids are kept in three identical cylindrical vessels A, B and C. The densities are ρA, ρB, ρC with ρA < ρB < ρC. The force on the base will be a. Maximum in vessel A

b. Maximum in vessel B

c. Maximum in vessel C

d. Equal in all the vessels

58. Statement (A): Pressure is a vector quantity.

Statement (B): Pressure P =F/A. Here F (Force) is a vector quantity. a. Both A and B are true

b. Both A and B are false

c. A is true and B is false

d. A is false and B is true

59. Statement (A): A closed compartment containing gas is moving with some acceleration in the horizontal direction. If the effect of gravity is neglected, then the pressure in the compartment will be higher on the rear side than on the front side.

Statement (B): Pascal's law holds only for a fluid at rest. a. Both A and B are true

b. Both A and B are false

c. A is true and B is false

d. A is false and B is true

60. A body will experience minimum upthrust when it is completely immersed in : a. turpentine

b. water

c. glycerine

d. mercury

61. The pressure P1 at a certain depth in river water and P2 at the same depth in seawater are related as : a. P1 > P2

b. P1 < P2

c. P1 = P2

d. P1 = P2 atmospheric pressure

62. Two balls, one of iron and the other of aluminium, experience the same upthrust when dipped in water if a. both have the same mass

b. one has half the volume of the other

c. both have equal volume

d. one has one-fourth the volume of the other

63. The surface of water in a tank on the top of a house is 4 m above the tap level. Then the pressure of water at the tap when the tap is closed will be a. 40000 Nm-2

b. 4000 Nm-2

c. 50000 Nm-2

d. 500 Nm-2

64. Two blocks of mass, 4 kg and 2 kg, are placed side by side on a smooth horizontal surface (as shown in the figure). A horizontal force of 20 N is applied on a 4 kg block. Find (i) The acceleration of each block (ii) normal reaction on block B due to A. A B 20 N 4 kg 2 kg

36

IL Foundation Series Class 8

a. 10/3 m/s2, 20/3 N

b. 15/3 m/s2, 25/3 N

c. 25/3 m/s2, 15/3 N

d. 20/3 m/s2, 10/3 N

65. Two masses, m1=5 kg and m2=4.8 kg tied to a string, are hanging over a light frictionless pulley. The acceleration of the masses when left free to move is [g=9.8 ms-2]

m1

a. 4.8 ms-2

m2

b. 9.8 ms-2

c. 5 ms-2

d. 0.2 ms-2

66. The upward acceleration of the 4 kg block in the shown figure (g=10 ms-2 )

4 kg a. 5 ms-2

F = 60 N

b. 15 ms-2

c. 25 ms-2

d. 10 ms-2

67. Assertion (A): Force cannot be added to pressure.

Reason (R): Force and pressure have the same dimensions. a. Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A). b. Both Assertion (A) and Reason (R) are true, but Reason(R) is not the correct explanation of Assertion (A). c. Assertion (A) is true but Reason (R) is false. d. Assertion (A) is false but Reason (R) is true 68. Assertion (A): Hydrostatic pressure is a vector quantity.

Reason (R): Pressure is a component of force divided by area, and force is a vector quantity. a. Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A). b. Both Assertion (A) and Reason (R) are true, but Reason(R) is not the correct explanation of Assertion (A).

37

FORCE AND PRESSURE

c. Assertion (A) is true but Reason (R) is false. d. Assertion (A) is false but Reason (R) is true 69. Assertion (A): Atmospheric pressure increases with increases in the depth of the sea.

Reason (R): Pressure is directly proportional to depth or height. a. Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A). b. Both Assertion (A) and Reason (R) are true, but Reason(R) is not the correct explanation of Assertion (A). c. Assertion (A) is true but Reason (R) is false. d. Assertion (A) is false but Reason (R) is true

38

2

FRICTION

2.1 FORCE OF FRICTION 2.1.1 Introduction to the force of friction Friction is a form of force which opposes the relative motion between the two surfaces in contact, and it acts on both surfaces. Friction is caused by the irregularities on the surfaces in contact. The force of friction generally increases if the two surfaces are pressed harder.

• Friction always opposes the relative motion of one surface over the other surface.

• Friction may oppose or support the motion of the body.

Example 1: A person is able to walk on the road because of friction. If there were no friction, his feet would slide back, and he would not be able to change his position.

Example 2: When a ball is rolling on a rough surface, it stops after some time because friction opposes motion.

Pushing Force Pushing Force

Motion Motion

Forceofoffriction friction Force Fig. 2.1 Force of friction

2.2 FACTORS AFFECTING FRICTION Friction is a result of the irregularities present on surfaces in contact with each other. Even seemingly smooth surfaces possess numerous minute irregularities. These irregularities interlock, necessitating the application of force to overcome this interlocking when attempting to move any surface.

39

FRICTION

The force of friction is influenced by the nature of the surfaces involved. Rough surfaces, with a higher density of irregularities, exhibit a greater force of friction compared to smoother surfaces.

Therefore, the force of friction tends to be more significant when dealing with rough surfaces.

The key factor contributing to friction is the interlocking of irregularities between the two surfaces.

As expected, the force of friction increases when more pressure is applied to these surfaces. This can be observed by the difference in the force required to drag a mat when it is unoccupied compared to when a person is sitting on it. The additional weight creates more pressure, leading to an increase in the force of friction.

Therefore, we can say that: • Friction depends on the nature of the surface in contact.

• Friction is independent of the area of contact.

• Friction depends on how hard the two surfaces press together.

Coefficient of friction: It is a measure that represents how much two objects resist sliding against each other. It is denoted by the symbol 'μ'(mu) and is calculated using the formula:

Force of Friction Normal Force • Here, the force of friction is the force resisting motion between two surfaces, and the normal force is the force exerted perpendicular to the surfaces in contact.

• Coefficient of friction (µ) =

2.3 FRICTION: A NECESSARY EVIL Friction is a necessary evil because it has both advantages and disadvantages.

2.3.1 Advantages and disadvantages of friction Advantages of friction

i. Safe walking on the floor is possible because of friction between the floor and the feet. ii. Nails and screws are held in the walls or wooden surfaces due to friction. iii. Friction helps the fingers to hold a drinking water tumbler or a pen. iv. Vehicles move on the roads without slipping due to friction, and they can be stopped due to friction.

Fig. 2.2 Advantages of friction

40

IL Foundation Series Class 8

Disadvantages of friction

i. F riction results in a large amount of power loss in engines and hence brings down their efficiency. ii. The wear and tear of the machines increases due to friction, reducing their life. iii. Friction causes unnecessary heating of the parts of the machinery, which may alter their operating conditions.

2.4 TYPES OF FRICTION 2.4.1 Static friction Static friction (FS): When a force tries to move an object at rest, then an opposing force parallel to the plane of contact may be developed. This force of friction is called static friction (FS).

The maximum static friction (Fms) is proportional to the normal reaction (N) on the body. ∴ Fms α N ⇒ Fms = µs N Here, the proportionality constant µs is called the coefficient of static friction.

Coefficient of static friction (μs)

Its value depends on the material and roughness of the two surfaces in contact.

It is a unitless and dimensionless quantity.

Note: As long as the normal force is constant, the maximum possible friction does not depend on the area of the surfaces in contact.

We know that µS N is the maximum possible force of static friction that can act between the bodies.

The actual force of static friction may be smaller than µS N , and its value depends on other forces acting on the body.

Thus fS ≤ fmax = µS N

SOLVED EXAMPLES Example 1: The coefficient of static friction between the block and rough horizontal surface shown in the figure is 0.6 and the normal reaction (N) on the block is 100 N. N p

fs mg

41

FRICTION

a. Find the maximum static friction that can act on the block. b. If the pulling force (P) on the block is 0 N, then find the nature and value of friction. c. If the pulling force (P) on the block is 20 N, then find the nature and value of friction. d. If the pulling force (P) on the block is 40 N, then find the nature and value of friction. e. If the pulling force (P) on the block is 60 N, then find the nature and value of friction. f. For what values of P does the body start moving?

Solution: a. Maximum static friction

fms = µs N = 0.6 ×100 N fms = 60 N b. Here pulling force (P) = 0 N < fms ∴ Nature of friction Static friction ( fS )

= Static = Pulling force =0N

Note: If a body is at rest and no force is applied to it, the force of friction (static) is zero. c. Here, pulling force (P) = 20 N < fms ∴ Nature of friction = Static Static friction (fs) = pulling force = 20 N d. Here, pulling force (P) = 40 N < fms ∴ Nature of friction = Static Static friction (fs) pulling force = 40 N e. Here, pulling force (P) = 60 N = fms ∴ Nature of friction = Static Maximum static friction (fms) = pulling force = 60 N In this case, the body is ready to move. f. If the pulling force is slightly greater than fms, i.e., 60 N, then the body starts moving.

From the above problem, it is clear that static friction is self-adjusting.

Example 2: A 5500 N force is applied to a sledge full of firewood in a snow-covered forest. The skis of the sledge have a coefficient of static friction µs =0.75 with the snow. If the fully loaded sledge has a mass of 700 kg, what is the maximum force of static friction?

Solution: N = mg (normal force) Fs (max) = µs N Fs (max) = µs mg 42 Fs (max) = (0.75)(700)(9.8) = 5145 N

IL Foundation Series Class 8

N = mg (normal force) Fs (max) = µs N Fs (max) = µs mg Fs (max) = (0.75)(700)(9.8) = 5145 N

2.4.2 Kinetic friction When a body moves on a rough surface, there may exist a frictional force parallel to the plane of contact. This force of friction is called Kinetic friction (fk), or sliding friction, or dynamic friction.

Kinetic friction (fk) on a body is directly proportional to the normal reaction (N) on the body. i.e., f K αN ⇒ f K = µk N

.....(i)

Here, the proportionality constant µ K is called the coefficient of kinetic friction.

• µ K value depends on the nature of the two surfaces in contact. If the surfaces are smooth, µ K will be small; if the surfaces are rough, µ K will be large. It also depends on the materials of the two bodies in contact.

• According to eq (i), the coefficient of kinetic friction does not depend on the speed of the sliding bodies. Once the bodies slip on each other, the frictional force is µ k N, whatever the speed. This is approximately true for relative speeds not too large (say for speeds < 10 ms −1 ).

• According to eq (i), as long as the normal force (N) is the same, the frictional force is independent of the area of the surface in contact.

• In general, µs is slightly greater than µ K. • µs is a unitless and dimensionless quantity.

Note: If nothing is said about the nature of friction, then we should assume that µs =µ K . In such a 0 case, we represent the coefficient of friction with µ = instead of µs (or) µ k .

1.

is 0unitless and dimensionless µ=

2.

is 0greater than or equal to zero µ=

3.

can µ= 0 be greater than 1

4.

cannot be less than zero µ= 0

5.

For smooth surface µ =0 For rough surface µ > 0

43

FRICTION

Frictional force

Distinction between static and kinetic friction

B C

E A Applied force

p

Q

Fig. 2.3 Variation of frictional force with applied force

When the body is at rest over the surface of another body, the frictional force increases from zero to maximum value with the pulling force. The variation of frictional force with the increase of pulling force is shown graphically in the figure. The frictional force increases with the pulling force from A to B when the body is at rest over the surface of another body. The frictional force is maximum at B. The dotted line BE represents the limiting frictional force. When the applied force (or) pulling force is increased beyond E, the frictional force decreases by a small amount, which is shown in the figure as BC. Then, the frictional force remains constant, which is represented by the line CP and is independent of the velocity. In this figure, PQ is the measure of kinetic friction, which will not increase even if the pulling force is increased. It is clear that PQ < BE, i.e. kinetic friction is less than maximum static friction (fk < fms) There are two primary types of kinetic friction: i. Sliding friction ii. Rolling friction Sliding friction involves the resistance experienced when one body slides over another, and it typically presents a greater challenge compared to rolling friction. Rolling friction, on the other hand, comes into play when an object rolls over a surface, and it is inherently lower than sliding friction. This distinction explains the preference for rolling, as exemplified by the invention of the wheel.

Fig. 2.4 Rolling friction and sliding friction

44

IL Foundation Series Class 8

To further enhance the advantages of rolling over sliding friction, many machines incorporate ball bearings. Ball bearings effectively replace sliding with rolling motion, significantly reducing friction.

A common application is found in the use of ball bearings between hubs and axles in ceiling fans and bicycles, where the benefits of rolling friction contribute to smoother operation and increased efficiency.

Example: A 20 kg block is in motion on a rough horizontal surface. A horizontal force of 60 N is required to keep the body moving at a constant speed. The coefficient of kinetic friction is _______.

( g = 10 ms ) −2

Solution: For a constant speed, the block should be in equilibrium, i.e., the net force acting on it should be zero.

F = Friction F = µmg

F µk = mg 60 60 = = = 0.3 mg 20 ×10

2.5 INCREASING AND REDUCING FRICTION In certain situations, friction is a desirable force serving specific purposes. For instance, the grooves on the soles of shoes and the treaded tyres of vehicles, like cars, trucks, and bulldozers, are designed to enhance grip on surfaces, ensuring safer movement. However, there are scenarios where minimising friction becomes essential.

The practice of sprinkling fine powder on a carrom board is a common example of intentionally reducing friction to increase efficiency.

Instances where deliberately increasing friction is necessary: • Brake pads in the brake systems of bicycles and automobiles are designed to intentionally increase friction. When the brake lever is pressed, these pads come into contact with the wheels, arresting the motion of the rim due to increased friction, ultimately stopping the wheel’s movement.

• Athletes in sports like kabaddi and gymnastics also manipulate friction deliberately for better performance. Kabaddi players rub soil on their hands to enhance grip, while gymnasts apply coarse substances to their hands for increased friction and improved grip.

45

FRICTION

2.5.1 Lubricants Lubricants, such as oil, grease, or graphite, minimise the interlocking of irregularities, enhancing the smoothness of motion. Applying a few drops of oil to door hinges, using grease in bicycles and motors, or employing graphite creates a thin layer between moving parts, preventing direct rubbing and ensuring smooth movement.

In some cases, alternative methods, like using an air cushion between moving parts, are employed to achieve the same friction-reducing effect.

Examples where lubricants are commonly used

• Automobile Engines: Motor oil is used to lubricate various engine components, such as pistons, camshafts, and bearings, ensuring smooth operation and reducing wear and tear.

• Door Hinges: Applying oil or grease to door hinges prevents squeaking and allows doors to swing smoothly.

• Bicycles: Grease is commonly applied to the chain and moving parts of bicycles to reduce friction and enhance overall performance.

• Industrial Machinery: In manufacturing settings, lubricants are used in heavy machinery, gears, and conveyor systems to minimise friction and heat generation.

• Bearings and Bushings: Lubricants are essential in maintaining the efficiency of bearings and bushings in various mechanical systems.

• Aircraft Components: Aviation lubricants are employed in aircraft engines and critical components to ensure reliable and efficient operation.

• Railroads: Lubricants are applied to rail tracks and switches to reduce friction and minimise wear in the railway system.

• Marine Equipment: Lubricants play a crucial role in marine applications, including ship engines, propellers, and winches.

• Household Appliances: Various household items, such as fans, blenders, and sewing machines, use lubricants to keep moving parts running smoothly.

• Power Tools: Lubricants are often applied to power tool components like gears and bearings to improve performance and extend the lifespan of the tool.

2.6 FLUID FRICTION A substance which has no definite shape and has the ability to flow is called fluid, for example, liquids and gases. Fluids exert force on objects as they move through them (liquid or gas).

Air, despite its light and thin composition, exerts a frictional force on objects navigating through it.

A similar principle applies to liquids like water, where the force of friction is evident as objects move through them.

2.6.1 Drag Drag is the frictional force exerted by fluids. It is influenced by various factors: • The speed of the object relative to the fluid 46

IL Foundation Series Class 8

• The object’s shape • The nature of the fluid itself These all contribute to the magnitude of this frictional force.

When objects traverse through fluids, they encounter resistance and consequently lose energy in the process. To counteract this energy loss, special shapes are imparted to objects, drawing inspiration from nature. Birds and fish, continually navigating through fluids, have evolved body shapes that minimise energy loss in overcoming friction. This design principle extends to human-made vehicles, such as aeroplanes, which share similarities in shape with birds.

2.6.2 Viscosity Imagine three tubes connected to a horizontal rod that you can rotate using a handle at one end, like in the figure below.

Crude Oil

Mercury

Water

Fig. 2.5 Viscosity

These tubes are closed at both ends and filled halfway with crude oil, mercury, and water. Look at the figure, and you'll see they're in the lower half of the tubes. Now, turn the handle to invert all the tubes. The liquids start flowing down, but they take different times to reach the bottom.

Apart from the friction between the glass surface and the liquids, there's also friction between the different layers of liquid, which resists their movement. This friction is called viscous force. Since the liquids take varying times to reach the bottom, it means the viscous force is different for each liquid. The less viscous force there is, the more mobile the liquid is. This special property of liquids is called viscosity.

Also, note that the viscosity of a liquid decreases as its temperature increases.

QUICK REVIEW • Friction is the form of force that opposes the relative motion between the two surfaces in contact, and it acts on both surfaces.

• Friction is caused by the irregularities on the surfaces in contact.

• The force of friction will increase if the two surfaces are pressed harder.

• Types of Friction: Friction has two types: static and kinetic.

• Static friction: Static friction comes into play to counterbalance the applied force on the body.

The maximum static friction (fms) is proportional to the normal reaction (N) on the body.

47

FRICTION

fms αN ⇒ fms = µs N • Kinetic friction: fK αN ⇒ fK = µk N • Sliding friction: When one surface is sliding over the other, sliding friction comes into play. The sliding friction is slightly smaller than the static friction.

• Rolling friction: When one body rolls over the surface of another body, the resistance to its motion is called rolling friction.

• Friction is a necessary evil, i.e., friction has both advantages and disadvantages.

• Friction can be reduced by using lubricants and by polishing the surface.

• Lubricants: The substances which reduce friction are called lubricants.

• It is always easier to roll than to slide a body over another.

• Rolling friction is smaller than sliding friction.

• Ball bearings reduce friction.

• Friction produces heat.

• Friction can't be entirely eliminated.

• No surface is perfectly smooth; some irregularities are always there.

• Drag is the frictional force exerted by fluids.

• Viscosity is the measure of a fluid’s resistance to flow.

WORKSHEET - 1 MULTIPLE CHOICE QUESTIONS WITH SINGLE CORRECT ANSWER I. Force of friction and factors affecting friction

1. The direction of frictional force with respect to the plane of contact (When two solid bodies are in relative motion) is a. Perpendicular

b. Parallel

c. Normal

d. Inclined

2. If a man is walking on the road, the direction of friction is a. Opposite to the direction of motion

b. Same as that of the direction of motion

c. Perpendicular to direction of motion

d. Inclined to the direction of motion

3. A body of mass 400 g slides on a rough horizontal surface. If the frictional force is 3 N, then the magnitude of contact force is (take g = 10 ms −2 ) a. 4 N

b. 3 N

c. 7 N

d. 5 N

4. A force of 98 newtons is required to pull a body of mass 1×102 kg over the surface of the ice, then the coefficient of friction is ( g = 9.8 ms −2 ) a. 0.2

48

b. 0.3

c. 0.1

d. 0.5

IL Foundation Series Class 8

5. A body of mass 100 g is made just to slide on a rough surface by applying a force of 0.8 N. Then the coefficient of friction is (Take g = 10 ms −2 ) a. 0.8

b. 0.08

c. 0.7

d. 0.6

6. The minimum force required to move a body of mass 5 kg over a surface whose coefficient of friction is 0.3 (g = 10 m/s2) a. 15 N

b. 13 N

c. 12 N

d. 10 N

7. A body just begins to slide over a rough surface when pulled with a force of 20 N. If it is pulled with a force of 15 N, the force of friction between the surfaces is a. Zero

b. 15 N

c. 20 N

d. 10 N

8. Which of the following statements is true? a. Coefficient of friction may be greater than unity b. Coefficient of rolling friction is less than that of kinetic friction c. The frictional force is independent of the speed of the body d. All of the above 9. Frictional force between two bodies depends upon a. Materials in contact b. Conditions of the sliding surfaces c. The force with which the two bodies are pressed d. All the above 10. When normal reaction is halved, the coefficient of friction is a. Halved

b. Unchanged

c. Doubled

d. Tripled

11. The limiting friction between two bodies in contact is independent of a. Nature of surface in contact

b. The area of surfaces in contact

c. Normal reaction between the surfaces d. All the above 12. Frictional force is a. Contact force

b. Gravitational force

c. Magnetic force

d. Weak force

II. Friction: A necessary evil

1. Assertion(A): Frictional force always opposes motion.

Reason(R): Frictional force is a non-conservative force. a. Both A and R are true, and R is the correct explanation of A b. Both A and R are true, and R is not the correction explanation of A c. A is true, R is false d. A is false, R is true

49

FRICTION

2. Assertion (A): Force of friction may oppose (or) support the motion of the body.

Reason (R): Force of friction does not oppose the motion of the body, but it opposes the relative motion between two bodies in contact. a. Both A and R are true, and R is the correct explanation of A b. Both A and R are true, and R is not the correction explanation of A c. A is true, R is false d. A is false, R is true III. Types of friction

1. A block of mass 2 kg is kept on the floor. The coefficient of static friction is 0.4. If a force F of 2 N is applied on the block, the frictional force between the block and the floor will be ( g = 10 ms−2 ) a. 2 N

b. 5 N

c. 8 N

d. 10 N

2. Assertion (A) : Static friction is a self-adjusting force.

Reason (R) : The magnitude of static friction is equal to the applied force, and its direction is opposite to that of the applied force. a. Both A and R are true, and R is the correct explanation of A b. Both A and R are true, and R is not the correct explanation of A c. A is true, but R is false d. A is false, but R is true 3. Assertion (A): The perpendicular component of contact force is called friction.

Reason (R): The angle between the resultant of normal reaction and the static frictional force with normal reaction is called the angle of friction. a. Both A and R are true, and R is the correct explanation of A b. Both A and R are true, and R is not the correct explanation of A c. A is true, but R is false d. A is false, but R is true 4. The maximum value of static friction that develops on a body when the body just tends to slide over the surface of another body is a. Kinetic friction

b. Rolling friction

c. Limiting friction

d. None of the above

5. The coefficient of static friction may be a. Less than 1

50

b. Greater than 1

c. Equal to 1

d. All the above

IL Foundation Series Class 8

6. Assertion (A): Frictional force increases with the increase of external force in the case of static friction.

Reason (R): Static friction is always equal to the applied force. a. Both A and R are true, and R is the correct explanation of A b. Both A and R are true, and R is not the correct explanation of A c. A is true, but R is false d. A is false, but R is true 7. Assertion (A): Static friction may not be proportional to normal reaction.

Reason (R): Static friction is self-adjusting. a. both A and R are true, and R is the correct explanation of A b. both A and R are true, and R is not the correct explanation of A c. A is true, R is false d. A is false, R is true.

8. Assertion (A): A car can run on a road because of the force applied by the road on the car.

Reason (R): Friction provides the necessary force for a translatory motion for a car starting from rest. a. Both A and R are true, and R is the correct explanation of A b. Both A and R are true, and R is not the correct explanation of A c. A is true, but R is false d. A is false, but R is true 9. Assertion (A): Kinetic frictional force opposes the relative motion of two bodies.

Reason (R): Frictional force is generated due to relative slipping. a. Both A and R are true, and R is the correct explanation of A b. Both A and R are true, and R is not the correct explanation of A c. A is true, R is false d. A is false, R is true 10. Assertion (A): When a block moves on a rough horizontal surface with some speed, it eventually slows down.

Reason (R): Friction always opposes motion. a. Both A and R are true, and R is the correct explanation of A b. Both A and R are true, and R is not the correct explanation of A c. A is true, R is false d. A is false, R is true 11. Mark the correct statement(s) about the friction between two bodies. i. Static friction is always greater than the kinetic friction.

51

FRICTION

ii. Coefficient of static friction is always greater than the coefficient of kinetic friction. iii. Limiting friction is always greater than kinetic friction. iv. Limiting friction is never less than static friction. a. i, ii, and iii

b. ii, iii, and iv

c. i and iv

d. ii and iii

12. Consider a vehicle going on a horizontal road towards the east. Neglect any force by the air.

The frictional forces on the vehicle by the road a. is towards the east, if the vehicle is accelerating b. is zero, if the vehicle is moving with a non-uniform velocity c. must be towards the east d. must be towards the west 13. Among the following, the correct statement(s) is/are a. µ is greater than (or) equal to zero

b. µ is less than (or) equal to zero

c. µ is always less than one

d. µ is always negative

IV. Increasing and reducing friction and fluid friction

1. A good lubricant should be highly a. Viscous

b. Non-volatile

c. High-density

d. None

2. Four children were asked to arrange forces due to rolling, static and sliding frictions in decreasing order. Their arrangements are given below. Choose the correct arrangement. a. Rolling, static, sliding

b. Rolling, sliding, static

c. Static, sliding, rolling

d. Sliding, static, rolling

3. Alida runs her toy car on a dry marble floor, a wet marble floor, a newspaper, and a towel spread on the floor. The force of friction acting on the car on different surfaces in increasing order will be: a. Wet marble floor, dry marble floor, newspaper and towel b. Newspaper, towel, dry marble floor, wet marble floor c. Towel, newspaper, dry marble floor, wet marble floor d. Wet marble floor, dry marble floor, towel, newspaper

WORKSHEET - 2 MULTIPLE CHOICE QUESTIONS WITH SINGLE CORRECT ANSWER 1. Force of friction has

52

a. Only advantages

b. Only disadvantages

c. Some advantages and some disadvantages

d. No advantages or disadvantages

IL Foundation Series Class 8

2. The use of lubricants is to a. Decrease friction

b. Increase friction

c. Make it stable

d. Make the engine more attractive

3. The force of friction a. Increases with the weight of the body

b. Decreases with the weight of the body

c. Is not affected by the weight of the body

d. None of these

4. The force of friction between two bodies is a. Parallel to the contact surface

b. Perpendicular to the contact surface

c. Inclined at 30° to the contact surface

d. Inclined at 60° to the contact surface

5. Friction can be reduced a. Using ball bearings

b. Using the lubricants

c. By polishing the surfaces in contact

d. All the above

6. If the normal reaction is doubled, the coefficient of friction is a. Doubled

b. Halved

c. Not change

d. Tripled

7. In the following forces of friction, the one which is self-adjusting is a. Rolling friction

b. Sliding friction

c. Static friction

d. Dynamic friction

c. Sliding friction

d. Fluid friction

8. Vehicles are streamlined to reduce a. Static friction

b. Kinetic friction

9. Ball bearings are used to a. Convert static to dynamic friction

b. Convert limiting to dynamic friction

c. Convert sliding to rolling friction

d. Convert rolling to fluid friction

10. The limiting friction is a. Equal to the dynamic friction b. Always less than the dynamic friction c. Always greater than the dynamic friction d. Sometimes greater and sometimes equal to dynamic friction 11. If nothing is said about the nature of friction, then a. µs =µ k

b. µs > µ k

c. µ k > µs

d. µs ≥ µ k

c. Equal to 1

d. All the above

12. The coefficient of static friction may be a. Less than 1

b. Greater than 1

53

FRICTION

13. A vehicle moves safely on a rough, curved and unbanked road, then a. The direction of static friction is radially outwards b. The direction of static friction is radially inwards c. The direction of kinetic friction is normal to a curved path d. Static friction does not exist 14. A block slides down a rough inclined plane. The work done by the force of friction on the block is: a. Zero

b. Positive

c. Negative

d. None of the above

15. The frictional force between two surfaces is independent of a. Nature of surface

b. Size of the body

c. Area of contact

d. Mass of the body

16. Let F,FN and f denote the magnitudes of the contact force, normal force and the friction exerted by one surface on the other kept in contact. If none of these is zero a. F > FN

b. F > f

c. FN - f < F < FN +f d. All the above

17. The contact force exerted by a body on another body is equal to the normal force between the bodies; we conclude that a. The surfaces must be frictionless b. The force of friction between the bodies is zero c. The bodies may be rough, but they don’t slip on each other d. Both b and c 18. Mark the correct statements about the friction between two bodies. a. Coefficient of static friction is always greater than the coefficient of kinetic friction b. Limiting friction is always greater than the kinetic friction c. Limiting friction is never less than static friction d. All the above 19. Assertion (A) : Static friction is a self-adjusting force.

Reason (R) : Kinetic friction does not depend upon the mass of the body. a. Both A and R are correct, and R is the correct explanation of A b. Both A and R are correct, but R is not the correct explanation of A c. A is correct, R is incorrect d. A is incorrect, R is correct 20. Assertion (A) : Frictional force is the component of contact force parallel to the surface.

Reason : Friction force always opposes the motion of the body. a. Both A and R are correct, and R is the correct explanation of A b. Both A and R are correct, but R is not the correct explanation of A c. A is correct, R is incorrect d. A is incorrect, R is correct 54

IL Foundation Series Class 8

21. Assertion (A) : When a bicycle is in motion, the force of friction exerted by the ground on the two wheels is always in the forward direction.

Reason (R) : Frictional force acts only when the bodies are in contact. a. Both A and R are correct, and R is the correct explanation of A b. Both A and R are correct, but R is not the correct explanation of A c. A is correct, R is incorrect d. A is incorrect, R is correct 22. The coefficient of friction depends on the i. nature of the surface ii. weight of the body iii. area of contact iv. material of the body a. (i), (ii) and (iv)

b. only (iv)

c. (i) and (iv)

d. (i) and (ii)

N

m

d. It is unitless

23. The SI unit of the static coefficient of friction is a. N

b. Nm

c.

24. The angle of friction ( γ ) and the coefficient of limiting friction ( µ ) are related as

1 1 b. tan γ = c. sin γ = d. γ = µ µ µ 25. The force of friction (f) and the normal reaction(R) between two surfaces in contact are related as a. tan γ = µ

a. f ∝

1

R

b. f ∝

1

R2

c. f ∝ R 2

d. f ∝ R

26. In a tug of war, the persons hold the two ends of a rope and try to pull the rope on their respective sides, then F

a. T = F

b. T > 2 F

T F

c. T < 2 F

d. T = 0

27. Friction is important for transport because a. All goods carriers move forward due to friction between tyres and road b. The sole of your shoes is grooved to provide shoes with a better grip on the floor so that you can move safely c. The tyres of cars, trucks and bulldozers are threaded to avail more support from friction to move. d. All the above 28. It is convenient for the luggage fitted with rollers to a. Push

b. Pull

c. Push or pull

d. None of these

55

FRICTION

29. The whirling speed of water gradually decreases, and after some time a. The frictional forces between the liquid layers are responsible for stopping the rotation of water. b. The frictional forces between the liquid surface that is in contact with the glass surface are responsible for stopping the rotation of water c. The gravitational forces between the liquid layers are responsible for stopping the rotation of water. d. The frictional forces between the liquid layers and between the liquid surface that is in contact with the glass surface are responsible for stopping the rotation of the water.

30. Choose the correct statement a. Friction can produce heat b. Friction can support the motion c. Friction opposes the relative motion between two surfaces in contact d. All the above 31. Friction is the opposing force or retarding force which comes into play a. When a body actually moves b. When a body tends to move over the surface of another body c. When we try to move one of the two objects, provided their surfaces are at rest relative to each other d. All of the above 32. The frictional force a. Always opposes the velocity of two surfaces b. Always opposes the relative motion of two surfaces of the bodies which are in contact c. It acts on both the surfaces d. Always opposes the relative motion of two surfaces of the bodies which are in contact and acts on both surfaces.

33. The friction which comes into play when the surfaces of the objects in contact are at rest relative to each other even after the application of force a. Static friction

b. Kinetic friction

c. Sliding friction

d. Fluid friction

34. The sliding friction is less than maximum static friction because a. Maximum static friction is due to the interlocking of irregularities in the two surfaces b. When the object starts sliding, the contact points on its surface do not get enough time to lock into the contact points on the floor c. When the object starts sliding, the contact points on its surface get enough time to lock into the contact points on the floor d. Both a and b

56

SOUND

3

3.1

INTRODUCTION TO SOUND

Sound is a type of energy that makes us hear things. It happens when air molecules move in a special way called waves. So, basically, sound is like a wave.

Sound is really important in our lives. It helps us communicate with each other, and we hear different kinds of sounds around us.

3.2

PRODUCTION OF SOUND

3.2.1 Sound is produced by a vibrating body Vibrating bodies produce sound. For example, when you pluck a guitar string, it starts to vibrate or shake back and forth really fast. Now, when it’s vibrating, it pushes the air around it. This pushing of air creates something we call sound waves. These sound waves travel through the air and reach your ears.

Vibrating prong

Tuning fork

When we beat a drum, its membrane vibrates to produce sound.

When we pluck the guitar strings, they vibrate and produce sound.

Prongs of a tuning fork produce sound when struck.

Fig. 3.1 Vibrating objects produce sound

So, in simple terms, sound is produced when something vibrates, like a guitar string, and the vibrations make the air around it move, creating sound waves that we can hear.

3.2.2 Sound produced by humans In humans, the sound is produced by the voice box known as the larynx, located in the upper part of the throat, just above the windpipe.

Within the larynx, there are two vocal cords with a narrow slit between them, allowing the passage of air. When the lungs expel air through the windpipe, it travels through this slit, leading to the

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production of sound as the vocal cords begin to vibrate. The muscles of the vocal cords also play a crucial role in sound production.

Fig. 3.2 Voicebox in humans

Quality: The quality or type of voice a person has is determined by the thickness and tightness of these vocal cords. In males, the vocal cords are approximately 20 mm long, while females have cords around 15 mm in length. Children, on the other hand, have shorter vocal cords.

As a result, the voices, their quality, and their characteristics differ among women, men, and children.

3.3

SOUND WAVES AND LIGHT WAVES

Waves in a medium can be classified into two main types: longitudinal waves and transverse waves.

3.3.1 Longitudinal waves In a longitudinal wave, the particles of the medium move parallel to the direction of the wave.

Regions where the coils are closer together are called compressions (C), and where they are further apart are called rarefactions (R) or expansion. Individual particles of the medium oscillate back and forth about their position of rest, contributing to the propagation of sound. Sound waves are an example of longitudinal waves.

Longitudinal wave

Wavelength Fig. 3.3 Longitudinal wave using spring

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3.3.2 Transverse waves In a transverse wave, particles of the medium oscillate up and down about their mean position as the wave travels. An example of a transverse wave is the ripples on the surface of water when a pebble is dropped into a pond. Light is also a transverse wave.

Wavelength

Transverse wave

Fig. 3.4 Transverse wave using spring

Note: Longitudinal waves involve the back-and-forth motion of particles along the direction of the waves. Transverse waves involve the up-and-down motion of particles perpendicular to the direction of the waves.

3.4

PROPAGATION OF SOUND

3.4.1 Sound needs a medium for propagation Sound travels in the form of mechanical waves that require a material medium for propagation.

It can move through solids, liquids, and gases. For instance, during an earthquake, shock waves originating from the earthquake’s epicentre travel in various directions. These waves pass through Earth’s layers, including solid rock materials and liquid water bodies. Upon reaching the Earth’s surface, the sound waves continue to travel through the air until they reach our ears, creating the sensation of hearing. This demonstrates that sound waves have the ability to traverse through solids, liquids, and gases.

3.4.2 Experiment to verify that sound requires a medium for propagation Consider an electric bell suspended within a glass jar equipped with an outlet. The bell is hung from the cork lid of the jar using strings, and two small holes in the lid allow for the connection of electric wires to the bell. Initially, the jar contains air. When the circuit is energised by turning on the switch, the bell rings, and the sound is audible to an observer standing in proximity to the jar.

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Lid made of cork Wires Electric bell Glass jar

Outlet to vacuum pump

Fig. 3.5 Bell-jar experiment

Subsequently, the outlet of the jar is attached to a vacuum pump, and the air is evacuated from the jar. Consequently, there is no longer air or any other medium surrounding the bell within the jar.

Upon activating the circuit, the bell still visibly rings, but the sound becomes inaudible. This shows that sound is unable to propagate through a vacuum.

3.5

SPEED OF SOUND

Sound moves through a medium, like air, at a certain speed. Interestingly, sound doesn’t travel as fast as light. We notice this when we see lightning (light) first and then hear the thunder (sound) a bit later. This tells us that sound is slower than light.

Let's take some examples to understand how sound moves through various mediums.

Example 1: When a person hits one end of the table, the resulting sound is almost instantly heard by another person placing their ear on the opposite end of the table. In comparison, if the same sound travels through the air, it takes considerably longer (approximately 14 times more time) to be heard across the same distance, with a notable reduction in intensity. Consequently, it is evident that sound travels more rapidly in solids than in gases or air.

Fig. 3.6 Sound in solids

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Example 2: When one of the two divers, submerged underwater and positioned at a significant separation, generates a sound, the other diver perceives it after a specific duration. In a parallel scenario above water, the same distance apart, if one of the individuals produces a sound, the other takes a slightly longer time to hear it than when underwater. This suggests that sound moves more swiftly in liquids than in gases or air.

Now, if the two divers underwater are situated at the ends of a lengthy metal rod and one taps the rod at their end, the other diver notices that they can hear the sound sooner if they place their ear against the rod. This observation indicates that sound travels faster in solids than in liquids.

In conclusion, the speed of sound is highest in solids, less in liquids, and least in gases or air. i.e., Speed of sound in Solids > Speed of sound in Liquids > Speed of sound in Gases The speed of sound is also influenced by the various properties of the medium it travels through like temperature. In general, as we raise the temperature of a medium, the speed of sound in that medium increases.

For instance, the speed of sound in air changes with temperature. At 0° C, it’s 331 metres per second, and at 22° C, it’s a bit faster at 344 metres per second.

State Solids

Liquids

Gases

Substance

Speed in m/s

Aluminium

6420

Nickel

6040

Steel

5960

Iron

5950

Brass

4700

Glass (Flint)

3980

Water (Sea)

1531

Water (distilled)

1498

Ethanol

1207

Methanol

1103

Hydrogen

1284

Helium

965

Air

346

Oxygen

316

Sulphur dioxide

213

Table 3.1 Speed of sound in different media at 25 °C

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3.6

CHARACTERISTICS OF A SOUND WAVE

3.6.1 Oscillatory motion and oscillation Oscillatory motion: When an object moves back and forth about a fixed point, it is described as having oscillatory motion.

and forth motion ofswing a Fig.Back 3.7 Oscillatory motion of a park park swing

Oscillation: Oscillation refers to the periodic movement of an object from one point to another. One oscillation is defined as the motion between the two extreme points or endpoints of the object.

Fig 3.8 Oscillation

3.6.2 Frequency, time period, and amplitude Frequency: The frequency of an object is the number of oscillations it completes per second. It is measured in Hertz (Hz), where 1 Hz equals 1 oscillation per second. For example, 30 Hz indicates 30 oscillations per second.

Low Frequency

High Frequency

Fig. 3.9 Frequency

Time period: The time required for one full oscillation of a sound wave is known as the time period of the sound wave.

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Period T

t

Time

Fig. 3.10 Time period

Amplitude: The amplitude of a sound wave is determined by the number of molecules it displaces from the mean position. It is defined as the maximum displacement of particles from their average position due to vibrations.

Amplitude

Time

Fig. 3.11 Amplitude

3.6.3 Loudness and pitch Loudness: The amplitude of vibration significantly influences the loudness of sound, with large amplitudes producing loud sounds and small amplitudes resulting in feeble sounds.

When the amplitude is greater, it leads to a larger displacement of particles, resulting in a louder sound. The relationship between the loudness of a sound and its amplitude is as follows: Loudness ∝ Amplitude2. The standard unit for measuring sound loudness is decibels (dB).

Wave disturbance Amplitude Time Soft sound Wave disturbance Amplitude

Time

Louder sound

Fig. 3.12 Loudness

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Normal breathing

10 dB

Soft whisper (at 5 m)

30 dB

Normal conversation

60 dB

Busy traffic

70 dB

Average factory

80 dB

Table 3.2 Loudness of different sounds

Note: Above 80 dB, the noise becomes physically painful.

Pitch: The pitch of a sound is influenced by the frequency of its sound wave. A higher frequency results in a higher pitch. Consider the comparison between the sound of a baby and that of an adult.

Despite having equal loudness, these sounds exhibit some differences.

Higher frequency leads to a shrill and higher-pitched sound, while lower frequency produces a lower-pitched sound. For instance, a drum, vibrating with low frequency, emits a low-pitched sound, while a whistle, with a high frequency, produces a higher-pitched sound.

Low frequency - Low pitch

High frequency - High pitch

Fig. 3.13 Pitch

3.7

AUDIBLE AND INAUDIBLE SOUNDS

In sound production, it is crucial to understand that a vibrating body is necessary. However, not all vibrations can be perceived by the human ear.

Sounds of frequencies less than about 20 vibrations per second (20 Hz) cannot be detected by the human ear. Such sounds are called infrasound. On the higher side, sounds of frequencies higher

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than about 20,000 vibrations per second (20 kHz) are also inaudible to the human ear. These sounds are called ultrasound.

Consequently, the human ear can detect sound in a frequency range of approximately 20 to 20,000 Hz, which are known as audible sounds.

Remarkably, certain animals, such as dogs, possess the ability to hear frequencies surpassing 20,000 Hz. This unique auditory capability is used by the police, who employ high-frequency whistles that are audible to dogs but not to humans. Other animals which rely on ultrasound are whales, bats, dolphins, etc.

Infra sound

Audible sounds

Ultra sound

Below 20 Hz

20 Hz to 20,000 Hz

Over 20,000 Hz

Fig. 3.14 Audible and inaudible sounds

3.8

THE HUMAN EAR

Sounds are generated as waves in the air or any medium they travel through. When these sound waves reach our ears, they undergo a transformation into electrical signals or messages comprehensible to the brain.

The specialised structure of our ears facilitates this process, comprising three main components: 1. Outer Ear (Pinna): This component captures sound waves and directs them to the subsequent part of the ear, namely the middle ear.

2. Middle Ear: Responsible for converting sound waves into vibrations, it achieves this with the assistance of the eardrum- a thin, rubber-like sheet located in the middle ear. When sound waves reach the eardrum, it vibrates, and these vibrations then travel to the inner ear.

3. Inner Ear (Cochlea): Here, the vibrations transmitted by the eardrum are received. The inner ear contains a liquid substance through which the vibrations move. Tiny hairs within the inner ear convert these vibrations into signals for the brain, which are transmitted to the brain through the hearing nerve. The brain promptly interprets the received signals as sound. However, this entire process occurs so rapidly that it goes unnoticed by our conscious awareness.

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Ear canal

Inner ear

Eustachian tube

Middle ear Eardrum

Pinna

Fig. 3.15 Structure of the human ear

3.9

REFLECTION OF SOUND

3.9.1 Reflection of sound Sound is like a bouncing ball, when it hits a solid or liquid, it bounces back, just like a rubber ball bounces off a wall. Similar to light, sound follows certain rules when it bounces off surfaces.

3.9.2 Laws of reflection of sound • The incident sound, the reflected sound, and the normal, all lie in the same plane.

• The angle of incident sound is equal to the angle of reflection formed by the reflected sound, i.e., i = r.

w nd ci

e av

w

de nt s

ou

d un

so

Normal

In

ed

ct

le

r

ef

i

R

av e

Reflecting surface

Fig. 3.16 Laws of reflection of sound

3.9.3 Echo Have you ever shouted or clapped near a big thing like a tall building or a mountain and heard your sound coming back to you?

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When a sound repeats itself in a place, we call it an echo. This echo happens because the sound bounces off surfaces and comes back to us. Our brain remembers the sound for a short time, about 0.1 seconds, and for us to hear a clear echo, the time between our shout and the echo must be at least 0.1 seconds.

Sometimes, if the sound bounces more than once, we might hear many echoes, one after the other.

If we assume the speed of sound is 344 metres per second, then the sound needs to travel back to our ears in 0.1 seconds to make the echo. That’s a total distance of at least (344 m/s) × 0.1 s = 34.4 metres. So, for us to hear a good echo, the object making the echo should be at least half of this distance away, which is 17.2 metres.

Echo Clap 17.2 m

Fig. 3.17 Echo

Note: Remember, this distance can change with the air temperature.

Example: A person clapped his hands near a cliff and heard an echo after 5s. What is the distance of the cliff from the person if the speed of the sound is taken as 346 m/s?

Solution: Given, Speed of sound, v = 346 m / s Time taken for hearing the echo, t = 5 s Distance travelled by the sound: velocity × time Distance v × t = 346 × 5 = 1730 m The echo has to travel twice the distance between the cliff and the person.

Hence, the distance between the cliff and the person is 1730 m/2 = 865 m.

3.9.4 Reverberation When a sound is made in a large hall, it keeps bouncing off the walls over and over until it becomes so quiet that we can’t hear it anymore. This prolonged bouncing and persistence of sound is known as reverberation.

Places like auditoriums and big halls often face this challenge. To manage reverberation, the roofs are made from soundproof materials like Fibreboard, and the chairs in the halls are covered with 67

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fabrics that can soak up sound. This way, the unwanted echoing is reduced, making it more pleasant for everyone in the hall.

ths

und Pa

ive So Reflect

Direct Sound Path

Fig. 3.18 Reverberation

3.10 NOISE AND MUSIC 3.10.1 Noise and music In our surroundings, we encounter various sounds, but not all sounds are pleasant. Consider construction work in your neighbourhood. The sounds emanating from the construction site are not enjoyable, and the honks of buses and trucks are unpleasant.

Sounds that are unpleasant are termed as noise.

On the flip side, the sounds of musical instruments are pleasant. Musical sounds are those that please the ear. The harmonium produces a musical sound, as does the string of a sitar. However, if a musical sound becomes excessively loud, it does not retain its melodious quality.

Musical sound

Noise

Fig. 3.19 Music and noise

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3.10.2 Noise pollution Certainly, you are already familiar with the concept of air pollution, characterised by the presence of undesirable gases and particles in the air. Likewise, the existence of excessive or unwanted sounds in our surroundings is termed noise pollution. Let’s explore some sources of noise pollution.

Major contributors to noise pollution include sounds generated by vehicles, explosions such as bursting crackers, various machines, and loudspeakers.

Reflecting on our homes, certain sources within them can also lead to noise pollution. This includes elevated volumes from devices such as televisions and transistor radios, certain kitchen appliances, desert coolers, and air conditioners. All of these contribute to the overall issue of noise pollution in our living environments.

Fig. 3.20 Noise pollution

3.10.3 Harms of noise pollution Excessive noise in our surroundings can have severe repercussions on our health. This includes issues like hypertension, insomnia, anxiety, memory impairment, stress, irritation, and even nervous breakdowns.

Furthermore, prolonged exposure to loud noises can cause temporary or permanent hearing loss in both humans and animals. The impact of excessive noise extends to affecting blood pressure, increasing cholesterol levels, and thereby elevating the risk of cardiovascular diseases.

It’s noteworthy that sound intensity exceeding 180 decibels can be fatal to a person. Noise pollution also disrupts the normal production of digestive juices in our bodies.

3.10.4 Measures to limit noise pollution To mitigate noise, it is essential to address its sources. Achieving this requires the installation of silencing devices in various settings, such as aircraft engines, transport vehicles, industrial machinery, and household appliances.

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Controlling noise pollution in residential areas involves strategic measures.

• Noisy activities should be conducted away from residential zones, and industries that produce significant noise should be established at a distance from such areas.

• Minimising the use of automobile horns, running TVs and music systems at low volumes.

• Planting trees along roads and around buildings can collectively reduce the impact of noise on residents.

These measures help attenuate the sounds reaching inhabitants, thereby diminishing the adverse effects of noise pollution.

QUICK REVIEW • Sound is a type of energy that makes us hear things. It happens when air molecules move in a special way called waves.

• A vibrating body produces sound.

• In humans, the sound is produced by the voice box known as the larynx, located in the upper part of the throat, just above the windpipe.

• Waves in a medium can be classified into two main types: longitudinal waves and transverse waves.

• In a longitudinal wave, the particles of the medium move parallel to the direction of the wave.

• In a transverse wave, particles of the medium oscillate up and down about their mean position as the wave travels.

• Sound travels in the form of mechanical waves that require a material medium for propagation.

• Speed of sound in Solids > Speed of sound in Liquids > Speed of sound in Gases • When an object moves back and forth, undergoing a vibrating motion, it is described as having oscillatory motion.

• Oscillation refers to the periodic movement of an object from one point to another.

• The frequency of an object is the number of oscillations it completes per second.

• The time required for one full oscillation of a sound wave is known as the time period of the sound wave.

• The amplitude of a sound wave is determined by the number of molecules it displaces from the mean position.

• The amplitude of vibration significantly influences the loudness of sound, with large amplitudes producing loud sounds and small amplitudes resulting in feeble sounds.

• The pitch of a sound is influenced by the frequency of its sound wave. A higher frequency results in a higher pitch.

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• The human ear can detect audible frequencies within the range of approximately 20 to 20,000 Hz, which are known as audible sounds.

• Sounds of frequencies less than 20 Hz or greater than 20,000 Hz are called inaudible.

• Parts of the Human ear - Outer Ear (Pinna), Middle Ear, and Inner Ear (Cochlea).

• Sound is like a bouncing ball - when it hits a surface, it bounces back.

• The incident sound, the reflected sound and the normal, all lie in the same plane.

• The angle of incident of incident sound is equal to the angle of reflection formed by the reflected sound, i.e., i = r.

• When a sound repeats itself in a place, we call it an echo.

• Prolonged bouncing and persistence of sound is known as reverberation.

• Sounds that are unpleasant are termed noise.

WORKSHEET - 1 MULTIPLE CHOICE QUESTIONS WITH SINGLE CORRECT ANSWER I. Introduction to sound and production of sound

1. _____________ helps to communicate with one another. a. Cloud

b. Sound

c. Bones

d. Rocks

c. Motion

d. Music

2. _____________ produces sound. a. Vibration

b. Force

3. In humans, sound is produced by _____________. a. Larynx

b. Anvil

c. Lungs

d. Windpipe

4. How many vocal cords are there in the human body? a. 3

b. 1

c. 2

d. 4

c. Esophagus

d. Trachea

5. What is the alternate name of the windpipe? a. Larynx

b. Anvil

6. When we speak, which part of our body vibrates? a. Vocal cords

b. Eyes

c. Nose

d. Brain

7. Which vocal folds' characteristic primarily determines the fundamental frequency and pitch of sound produced by humans? a. Length of the vocal tract

b. Length and tension of the vocal folds

c. Shape of the nasal cavity

d. Size of the oral cavity

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8. The length of the vocal cord is maximum for: a. Men

b. Women

c. Children

d. Adolescent boys

II. Sound waves and light waves, propagation of sound and speed of sound

1. The correct statement is: a. Sound and light both require a medium for propagation. b. Sound can travel in a vacuum, but light cannot. c. Sound needs a medium, but light does not need a medium for its propagation. d. Sound and light both can travel in a vacuum.

2. A sound requires _____________ for propagation. a. Medium

b. Vibration

c. Motion

d. Contact

c. Air

d. Space

3. It is impossible for sound to travel through: a. Stone

b. Water

4. In which of the following mediums does sound propagate at a higher speed? a. Solids

b. Liquids

c. Gases

d. Air

5. A ringing alarm clock is placed inside a sealed glass container. If the container is evacuated to create a vacuum, what do you think will happen to the audibility of the alarm sound inside and outside the container? a. The alarm sound will be louder inside the evacuated container and inaudible outside the container. b. The alarm sound will be inaudible both inside and outside the evacuated container. c. The alarm sound will be louder both inside the evacuated container and outside the container. d. The alarm sound will be inaudible inside the evacuated container but audible outside the container.

6. The speed of sound in air at room temperature is approximately 343 metres per second. If the speed of sound in water is 1482 metres per second, what is the speed of sound in steel (approximate value) at the same temperature? a. Less than 1482 m/s

b. Equal to 1482 m/s

c. More than 1482 m/s

d. Can’t determine

7. What happens to the speed of sound in the air if the temperature is increased? a. It increases

b. It decreases

c. It remains the same

d. It depends on the frequency of the sound

8. The speed of sound in air is approximately _____________ 72

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a. 340 m/s

b. 3400 m/s

c. 34 m/s

d. 3.4 m/s

III. The human ear and characteristics of a sound wave

1. In the human ear, sound vibration makes the _____________ vibrate. a. Eardrum

b. Membrane

c. Cochlea

d. Larynx

2. Which structure in the inner ear is responsible for converting sound vibrations into nerve impulses or electrical impulses? a. Eustachian tube

b. Cochlea

c. Semicircular canals d. Vestibule

3. Which of the following is the unit of measurement of frequency? a. Metre

b. Second

c. Hertz

d. newton

4. 1 Hertz is equal to: a. 1 vibration per minute

b. 10 vibrations per sec

c. 60 vibrations per minute

d. 6 vibrations per sec

5. The loudness of sound is determined by its _____________. a. amplitude of vibration b. ratio of amplitude and frequency of vibration c. frequency of vibration d. product of amplitude and frequency of vibration 6. In order to reduce the loudness of a sound, we have to _________________. a. decrease the frequency of vibration of the sound b. increase its frequency of vibration of the sound c. decrease its amplitude of vibration of the sound d. increase its amplitude of vibration of the sound 7. Small amplitude of sound vibrations will produce _____________. a. Loud sound

b. Feeble sound

c. Shrilled sound

d. Fast sound

8. The loudness of sound is measured in which of the following units? a. Centimetre

b. Joule

c. Decibels

d. newton

c. Amplitude

d. Timbre

c. mid

d. zero

9. What determines the pitch of sound? a. Frequency

b. Time period

10. A lion makes a __________ pitched roar. a. low

b. high

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11. Which of the following is correct about stringed instruments if you pluck the string in the middle with a force of greater magnitude and then with a smaller magnitude? a. The amplitude of a string is larger when it is plucked with a greater force. b. The amplitude of a string is smaller when it is plucked with a greater force. c. The amplitude of a string is larger when it is plucked with a weaker force. d. There is no amplitude in either case.

IV. Audible and inaudible sounds, reflection of sound, and noise and music

1. A human ear cannot hear a sound with a frequency greater than: a. 10,000 Hz

b. 20000 Hz

c. 5000 Hz

d. 15000 Hz

2. A sound of frequency less than 20 Hz is called ____________ sound. a. Ultrasonic

b. Infrasonic

c. Audible

d. Supersonic

c. Subsonic

d. Supersonic

3. Bats produce which of the following sounds? a. Infrasonic sound

b. Ultrasonic sound

4. The sound limit between the frequency of 20 Hz - 20000 Hz is called as a. Audible range

b. Ultrasound range

c. Low sound range

d. Supersonics

5. When a sound wave hits a barrier, it __________ a. Bounces back

b. Decreases

c. Increases

d. Stops

6. In an experiment on studying the laws of reflection of sound, the tube facing the clock is placed as shown. The position of the second tube, at which the ear will get the best-reflected sound, is obtained when θ equals _____________.

40° θ

Clock a. 20o

b. 30o

Ear c. 40o

d. 50o

7. To hear a distinct echo, the time interval between the original sound and the reflected one must be at least _________. a. 0.1 s

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c. 10 s

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8. An echo was heard after 3 seconds. How far away from the source is the reflecting surface if sound travels at a speed of 342 m/s? a. 1026 m

b. 126 m

c. 513 m

d. 51 m

9. The sound of a drill machine and car honking is _________. a. Unpleasant

b. Pleasant

c. Both pleasant and unpleasant

d. Unpleasant in certain situations

WORKSHEET - 2 MULTIPLE CHOICE QUESTIONS WITH SINGLE CORRECT ANSWER 1. Sound waves are a. Transversal waves

b. Longitudinal waves c. Both a & b

d. None of these

2. Velocity of sound is maximum in a. Air

b. Wood

c. Vacuum

d. Iron

c. Zero

d. None of these

3. Velocity of sound in vacuum is a. Maximum

b. Minimum

4. If a pendulum oscillates 50 times in 10 seconds, then time period is

1 s 5

b. 5 s

a. Frequency

b. Echo

a.

c. 500 s

d. 100 s

c. Amplitude

d. None of these

c. < 20 Hz

d. > 20 KHz

c. 3×1010 ms -1

d. 500 ms -1

c. 17-25 mm

d) 25-50 mm

c. Both (a) & (b)

d. None of these

5. The reflection of sound from an obstacle is 6. The range of infrasonic sound is a. 20 Hz

b. > 20 Hz

7. Speed of sound is approximately: a. 3×108 ms -1

b. 340 ms -1

8. The length of the vocal cord in man is a. 0-10 mm

b. 10-15 mm

9. A sensation depending upon the frequency is a. Pitch

b. Amplitude

10. Harmful intensity of sound is ___________. [dB ] a. 0

b. 60

c. above 80

d. 50

11. A tuning fork sends sound waves in the air. If the temperature of the air increases, which of the following parameters will change? a. Displacement amplitude

b. Frequency 75

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c. Wavelength

d. Time period

12. When a sound wave is refracted from air to water, which of the following will remain unchanged? a. Wave number

b. Wavelength

c. Wave velocity

d. Frequency

c. Metre

d. Metre/second

13. The SI unit of frequency is a. Hertz

b. Second

14. An instrument used to produce fixed frequency in the physics laboratory is a. Simple pendulum

b. Thermometer

c. Tuning fork

d. An electric bell

15. Distance between two consecutive rarefaction is a. Amplitude

b. Wavelength

c. Frequency

d. Pitch

c. Loudness

d. Quality

c. Wood

d. All the above

16. The frequency of a sound wave describes its a. Speed

b. Pitch

17. Sound can travel through a. Air

b. water

18. In stringed instruments, the frequency of sound produced depends on the a. length of wire/string

b. thickness of wire/string

c. tightness of string

d. all the above

19. The Human ear can hear two sounds separately and distinctly if they are separated by a time interval of a. 1/10 second

b. 1 second

c. 0.01 second

d. 0.001 second

20. When you speak to your friend, which of the following parameters has a different value in the sound produced? a. Frequency

b. Wavelength

c. Amplitude

d. All the above

21. Sound can travel through a. Gases only

b. Solids only

c. Liquids only

d. Solids, liquids and gases

22. In which part of the ear sound is magnified a. Outer

b. Middle

c. Inner

d. None

c. Wavelength

d. None

c. Child

d. Insect

23. The loudness of the sound depends upon a. Amplitude

b. Frequency

24. Which one has more pitch ? a. Man

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25. The unit of sound intensity a. Hertz

b. Metre

c. Decibel

d. Cycle / Second

26. In which of the following, sound propagation is more? a. Solids

b. Liquids

c. Gases

d. None of these

27. Which part of the tabala vibrates and produces sound ? a. Membrane

b. String

c. Metal frame

d. All the above

28. Example for musical instrument in which strings vibrate a. Tabla

b. Mridangum

c. Flute

d. Sitar

29. Sound is produced a. When a metal object is hit by a hammer (or) when it falls onto a hard concrete floor b. When air is blown into the papers of your notebook c. When we pluck a rubberband fixed between two rigid supports d. All the above 30. The musical instruments that produce sound by vibrating different parts of them a. Tabla

b. Flute

c. Guitar

d. All the above

31. In Jaltarang, we observe a. Bowls containing water in increasing order produce different sounds upon striking gently with spoon. b. Bowls containing water at the same level are producing the same sound upon striking gently with spoon. c. We observe the variation of sound due to change in the water level of the bowl d. All the above 32. Choose the correct statements a. Sound can travel from one place to another b. Air surrounding us acts as a medium c. In solids, sound travels with high speed when compared with liquids and gases d. All the above 33. Sound pollution can be controlled by a. Removing silencers of bikes and other machines b. Manufacturing machines that work with high noise c. Using TVs and tape recorders with high volume d. Plant trees to reduce sound pollution 77

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34. Sound pollution causes a. First effect is loss of hearing

b. Sleeplessness and hypertension

c. Increase in blood pressure and headache

d. All the above

35. Choose the correct statement a. Long hack-saw blade, which is fixed at one end, produces less number of oscillations up on plucking and produces a shrill sound. b. Small hexa blade, which is fixed at one end, produces more number of oscillations up on plucking and produces a shrill sound. c. Long hack-saw blade, which is fixed at one end, produces more number of oscillations up on plucking and produces a flat sound. d. Small hexa blade, which is fixed at one end, produces less number of oscillations up on plucking and produces a shrill sound.

36. Choose the correct statement a. Humans and animals have a mechanism of communication by producing sounds with different frequencies and amplitudes according to their needs. b. A word is a sound of mixed frequencies. c. Sound pollution is a serious problem like air/water pollution. d. All the above 37. There are many sounds causing sound pollution, like a. Sounds of traffic, sounds by motorbikes, bike horns b. Sounds at industries c. Sounds during explosions, sounds during the bursting of crackers d. All the above 38. Choose the correct statement a. Our ear consists of two sections: the outer ear and inner ear b. Pinna of the external ear collects the sound vibrations c. The sound vibrations collected will enter into the inner ear d. All the above 39. The middle ear a. contains three small bones

b. contains two small bones

c. contains four small bones

d. none of these

40. The middle ear contains the following shaped bones a. Malleus 78

b. Incus

c. Stapes

d. All the above

IL Foundation Series Class 8

41. In the middle ear, the bones which magnify the sound vibrations are a. Malleus

b. Incus

c. Stapes

d. All the above

42. Bones that transmit the vibrations from the middle ear to the membrane of oval window are a. Malleus

b. Incus

c. Stapes

d. Both a & b

43. The cochlea is a. the inner part of the ear

b. which is filled with fluid

c. transmits vibrations

d. all the above

44. Choose the correct statements a. Larynx is the important organ in human body to produce sound b. Larynx has two muscular ligaments at the end of wind pipe called vocal cords c. Vocal cords are stretched across voice box, it leads to a narrow slit between them to allow passage of air d. All the above 45. When we speak a. The vocal cords open

b. Vocal cords close

c. Vocal cords open and close

d. None of these

46. Louder sound will be produced a. by blowing air forcibly onto the vocal cord b. by getting the voice box really tensed c. both a and b d. by blowing air normally onto the vocal cord 47. Assertion (A): When lightning strikes, the sound is heard a little, after the flash is seen.

Reason (R): The velocity of light is greater than that of the sound. a. Both A and R are correct and R is the correct explanation of A b. Both A and R are correct but R is not the correct explanation of A c. A is correct, R is incorrect d. A is incorrect, R is correct 48. Assertion (A): Sound waves cannot propagate through a vacuum, but light waves can.

Reason (R): Sound wave cannot be polarised but light waves can be polarised a. Both A and R are correct and R is the correct explanation of A b. Both A and R are correct but R is not the correct explanation of A c. A is correct, R is incorrect 79

SOUND

d. A is incorrect, R is correct 49. Assertion (A): Noise pollution is an unwanted accumulation of noise in the atmosphere.

Reason (R): It interferes with communication. a. Both A and R are correct and R is the correct explanation of A b. Both A and R are correct but R is not the correct explanation of A c. A is correct, R is incorrect d. A is incorrect, R is correct

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4

CHEMICAL EFFECTS OF ELECTRIC CURRENT

Electricity powers our world, making our lives brighter, more connected, and more efficient. It's the invisible force that fuels our homes, drives our technology, and sparks innovation. But behind its everyday magic lies a fascinating journey of understanding its effects. Let us explore the chemical effects of electricity in this chapter.

4.1 CONDUCTORS OF ELECTRICITY 4.1.1 Electricity Electricity can be defined as a form of energy generated by the movement of electric charges. There are two types of electric charges present in nature.

1. Positive charges (protons) 2. Negative charges (electrons) In an atom, both types of charges exist. Electrons are lighter and relatively free, while protons are heavy and fixed in their position. So, the current flows mainly due to the flow of electrons. The continuous flow of charge per unit of time is called electric current.

Electrons move from a body with an excess of electrons to one with a lesser number of electrons. The current always flows in the opposite direction to the flow of electrons, which is known as the direction of conventional current.

Conventional current flow

Electron flow

-

+

Fig. 4.1 Flow of electrons in a circuit

Now, based on the conductivity, substances can be classified into two types - conductors and insulators

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CHEMICAL EFFECTS OF ELECTRIC CURRENT

4.1.2 Conductors and Insulators Conductor: A conductor is a material or substance that allows electricity to pass through it.

Conductors allow the movement of charges through them. The electrons can freely flow as they are delocalised and hence can take electric current through them.

For example, metals like gold, silver, copper, etc., are good conductors.

Insulator: An insulator is a substance or material that does not allow the flow of electricity to pass through it. They do not allow the flow of charges through them as their electrons are tightly packed within, and there are very few electrons available for the conduction of electricity.

For example, rubber, glass, wood, plastic, and ceramics are insulators.

Water

Gold

Oil

Cork

Steel

Copper

Rubber

Glass

Fig. 4.2 Conductors and insulators

4.2 DO LIQUIDS CONDUCT ELECTRICITY? Often, during rainy seasons, we are asked to stay away from the electric poles. Have you ever wondered why it is so? This is because water is a good conductor of electricity. If there is a fault in the electrical system, such as a damaged wire or faulty insulation, it can facilitate the flow of electricity to the ground, posing a risk to anyone in contact with the water or the wet surroundings.

Most liquids conduct electricity as they have free ions or electrons, which carry the electricity through them. Because they conduct electricity, solutions of bases, acids, and salts in water are referred to as electrolytes. For example, lemon juice, sodium hydroxide, tap water, milk, and vinegar.

Distilled water is a poor conductor of electricity because it lacks salts and, hence, does not conduct electricity. Oils, gasoline, and kerosene are also poor conductors of electricity.

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IL Foundation Series Class 8

Good conductor/ Poor conductor

Material Distilled water

Poor conductor

Tap water

Good conductor

Lemon juice

Good conductor

Vinegar

Good conductor

Cooking oils

Poor conductor

Milk

Good conductor

Honey

Poor conductor

Mercury

Good conductor

Fuels

Poor conductor

Table 4.1 Liquids that are good or poor conductors of electricity

4.2.1 How do liquids conduct electricity?

When various substances are dissolved in water, and an electric current is passed through the solution, the components of these substances can undergo ionisation, i.e., breaking apart into positive and negative ions in the water.

• This ionisation allows the solution to conduct electricity.

• The conductivity of a solution is closely related to the concentration of ions within it. A higher concentration of ions generally results in better electrical conductivity.

Fig. 4.3 Electricity through liquid

• For instance, distilled water is a poor conductor of electricity because it lacks significant concentrations of ions. On the other hand, saltwater is a good conductor as the dissolved salt (sodium chloride) dissociates into sodium ions and chloride ions.

• Certain compounds do not readily form ions when mixed with water, leading to poor electrical conductivity. Examples of such substances include sugar dissolved in water, oil, and alcohol.

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CHEMICAL EFFECTS OF ELECTRIC CURRENT

LED bulbs are more suitable for testing the electrical conductivity of liquids

• The heating effect of the electric current often causes the bulb's filament to heat up and glow.

• While some liquids can carry electricity, their electrical conductivity is usually weak. Hence, when the current passes through them, it is not strong enough to heat the filament. Therefore, the filament does not light up in the case of such liquids.

• On the other hand, even minute amounts of electrical current are detected by the LED lamps. LED lights can, therefore, be used for measuring the electrical conductivity of liquids.

Fig. 4.4 LED

4.3 CHEMICAL EFFECTS OF ELECTRIC CURRENT When an electric current is passed through a conducting solution or an electrolyte, the resulting chemical changes are known as the chemical effects of electric current. Chemical reactions occur when an electric current passes through a solution.

Electrolysis is one of the many phenomena based on the chemical effects of electric current.

4.3.1 Electrolysis Electrode: An electrode can be defined as a conductor of electricity that can carry electric current into non-metals and other poor conductors of electricity.

Cathode and Anode

• The electrode connected to the battery's negative terminal is referred to as the cathode (negative electrode).

• The electrode connected to the battery's positive terminal is referred to as the anode (positive electrode).

Electrolytes: Electrolytes can be defined as liquids that facilitate the flow of electricity and undergo a process of separation (splitting) of ions when an electric current is applied to them. They are the conducting solutions.

Electrolysis: is the process in which an electric current passes through the electrolyte, causing the molecules within the liquid to dissociate into positively and negatively charged ions.

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IL Foundation Series Class 8

DC current

-

+

-

Cathode

+ +

Cation

-

Anode Anion

- + - + + - + -

+

Electrolyte

Fig. 4.5 Electrolysis

4.3.2 Electrolysis of NaCl When electricity is passed through a solution of NaCl (as an electrolyte), the following products are formed at the electrodesIn the solution, there are Na+, Cl-, H+, and OH- ions.

H+ is discharged at the cathode, whereas Cl- is discharged at the anode.

Reaction at the cathode: 2H+ + 2e- → H2 (g) Reaction at the anode: 2Cl- → Cl2 (g) + 2e-

The following effects can be observed in the solution during electrolysis: • Deposition of metal coatings on the electrodes • Alteration in the colour of the solution • Liberation of gas or formation of bubbles within the solution Applications of electrolysis

• Electroplating • Purification of the metals • Metal extraction from metallic ores

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CHEMICAL EFFECTS OF ELECTRIC CURRENT

4.4 ELECTROPLATING 4.4.1 What is electroplating?

Electroplating is a technique to deposit a layer of metal on another material using electricity.

Electroplating is a common process in many industries where a metal layer with certain properties is applied onto another metal surface. Metals like nickel, copper, gold, silver, tin, brass, zinc, chromium, and platinum are often used in electroplating.

Process of electroplating: To conduct the process of electroplating, the right electrodes and electrolytes must be chosen so that metal can be deposited over a material. For example, to deposit copper on a material, the electrolyte should contain copper in it. Similarly, if gold on a material is needed, an electrolyte that contains gold should be used. It is important to ensure that the electrode selected is completely clean.

• Different materials make up the electrodes used during the process of electroplating. One electrode shares the same metal composition as the electrolyte solution.

• The second electrode should be the material intended for coating with another metal. For instance, to plate brass with copper, one electrode should be copper and the other brass, while the electrolyte solution could be copper sulphate.

• In this setup, the copper electrode functions as the anode (positive), and the brass electrode serves as the cathode (negative).

• When electricity passes through the solution, copper sulphate breaks down into its ions.

• Positively charged copper ions are attracted to the brass electrode, while negatively charged sulfur ions migrate toward the copper electrode. As a result, copper starts depositing on the brass electrode.

The process of electrolysis is represented as follows At the anode (Copper Electrode - Positive) Cu → Cu2+ + 2eAt the cathode (Brass Electrode - Negative) Cu2+ + 2e- → Cu

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IL Foundation Series Class 8

- +e

-

eCathode

+

-

Brass

Anode

Cu

Cu2+ SO42-

Impurities (anode mud)

Copper Plating Fig. 4.6 Electroplating

Electroplating takes time to complete. The duration usually depends on how strong the electric current is and how concentrated the electrolyte is. If we increase both, the electroplating happens faster.

4.4.2 Applications of electroplating • Medical tools, usually made of nickel, get coated with platinum or gold.

• Items like kitchen tools, bathroom taps, and car parts get covered with a layer of chromium to protect them. Since chromium is expensive, objects are first made from cheaper metals and then coated with chromium.

• Jewellery designers often use cheaper metals to create ornaments and then add a layer of gold or silver.

• Tin cans for storing food are made of iron but coated with tin to prevent food spoilage caused by iron reacting with it.

• Bridges and car parts are made of iron for strength. To stop them from rusting, they're coated with zinc, a process called galvanisation.

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CHEMICAL EFFECTS OF ELECTRIC CURRENT

Kitchen stove

Bicycle handle

Tap

Bicycle bell

Wheel rims

Car grill

Fig. 4.7 Some electroplated objects

QUICK REVIEW • Electricity can be defined as a form of energy generated by the movement of electric charges.

• A conductor is a material or substance that allows electricity to pass through it.

• An insulator is a substance or material that does not allow the flow of electricity through it.

• Some liquids are good conductors of electricity, and some are poor conductors.

• Most liquids that conduct electricity are solutions of acids, bases, and salts.

• The passage of an electric current through a conducting liquid causes chemical reactions.

The effects are called the chemical effects of currents.

• Electrolysis is the production or occurrence of chemical change in an electrolyte when an electric current is passed through it.

• The process of depositing a layer of any desired metal on another material using electricity is called electroplating.

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IL Foundation Series Class 8

WORKSHEET - 1 MULTIPLE CHOICE QUESTIONS WITH SINGLE CORRECT ANSWER I.

Conductors and insulators

1. Polythene is a: a. A conductor

b. An insulator

c. A semiconductor

d. A metal

2. Which among the following is a conductor? a. Brass

b. Plastic

c. Mica

d. Leather

3. The material that allows electric current to pass through it is called: a. An insulator

b. A conductor

c. Both a and b

d. None of these

4. The material that does not conduct electric current is called: a. An insulator

b. A solution

c. A metal

d. An electrolyte

5. Which among the following is a conductor? a. Comb

b. Glass

c. Balloon

d. Iron nail

6. All metals are a. Insulators

b. Conductors

c. Electrolytes

d. None of these

7. Electricians use rubber gloves while working because: a. Rubber is an insulator b. Rubber is a good conductor c. It is easy to work while wearing gloves d. None of these 8. Which of the following is an insulator? a. Tyres

b. Steel rod

c. Gold chain

d. Iron rod

9. Common salt in solid form acts as: a. An insulator

b. A conductor

c. An electrolyte

d. None of these 89

CHEMICAL EFFECTS OF ELECTRIC CURRENT

10. You are cautioned not to touch electrical appliances with wet hands because: a. It may cause an electric shock to your body b. It can damage the appliance c. It may burn out d. None of these II. Do liquids conduct electricity?

1. ______ do not readily form ions when mixed with water, leading to poor electrical conductivity. a. NaCl

b. Copper Sulphate

c. Sugar

d. All of the above

2. Which of the following cannot conduct electricity? a. Petrol

b. Lime juice

c. Tap water

d. Salt-water

3. The magnetic compass is used to check: a. Small current

b. Slow current

c. Magnetism

d. Both a and c

4. Which type of solution conducts electricity? a. Acids

b. Bases

c. Salts

d. All of the above

5. LED has the capability of: a. Glowing even though there is no current b. Glowing even though there is a small current c. Glowing when there is a specific current d. All of the above 6. Most liquids that conduct electricity are _____________. a. Solutions of acid

b. Solutions of bases

c. Solutions of salts

d. All of the above

7. Distilled water is a poor conductor of electricity because ______________. a. It is pure b. It is free from all salts, minerals, and acids c. It does not contain any ions d. All of the above

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IL Foundation Series Class 8

8. Any liquid that conducts electricity contains: a. Un-dissociated molecules

b. Dissociated ions

c. Special molecules

d. All of the above

9. Which of the following is the best conductor of electricity? a. Honey

b. Distilled water

c. Sea-water

d. Oil

10. In a cell, electrons move from: a. The positive electrode to the negative electrode b. The negative electrode to the positive electrode c. Both a and b d. Electrons do not move, and only negative charge moves from one place to another place III. Chemical effects of electric current

1. During the electrolysis of water, the gas released at the cathode is _____________. a. Oxygen

b. Hydrogen

c. Both oxygen and hydrogen

d. None of these

2. Which of the following substances is used in electrolytes? a. Copper

b. Copper sulphate

c. Mercury

d. Kerosene

3. The liquid which conducts electricity and undergoes decomposition is called ____________. a. Electrolyte

b. Electrode

c. Electrolysis

d. Non - electrolyte

4. In the electrolysis of copper sulphate solution, copper metal forms on the ______________. a. Cathode

b. Anode

c. Cation

d. Anion

5. During electrolysis, the electrolyte undergoes ______________. a. A physical change

b. A chemical change

c. Either a or b

d. None of these

6. An electrolyte is a. A metal

b. A solution

c. non-metal

d. A liquid that conducts electricity

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CHEMICAL EFFECTS OF ELECTRIC CURRENT

7. When a zinc and a copper plate are placed in dilute sulphuric acid, we observe that: a. Copper slowly dissolves in the sulphuric acid b. Zinc slowly dissolves in the sulphuric acid c. Bubbles form on the copper rod d. Both b and c 8. The electrodes are: a. Conductors through which electricity enters b. Conductors through which electricity leaves c. Conductors which produce electricity d. Conductors through which electricity enters or leaves 9. In an electric cell: a. The metal used in the cathode should have high reactivity when compared with metal ions present in the electrolyte b. The metal used in the anode should have less reactivity when compared with the metal used in the cathode c. The electrolyte should allow the displacement reactions d. All of the above 10. Which of the following statements is true? a. Electrolysis is one of the applications of chemical effects of current. b. A metal wire shows a chemical effect when a current is passed through it. c. Like charges attract each other. d. Charge flows only through negative charge carriers.

IV. Electroplating

1. A charge carried by anions is ________________. a. Negative

b. Positive

c. Positive or negative

d. None of these

2. The object to be electroplated is placed at the___________. a. Anode

b. Cathode

c. Anode or cathode

d. None of these

3. A positively charged ion is called ___________.

92

a. Cation

b. Anion

c. Atom

d. Neutron

IL Foundation Series Class 8

4. Which process is performed to prevent corrosion of iron objects? a. Electrolysis

b. Refining

c. Electroplating

d. Metallurgy

5. Assertion (A): Iron sheets and water pipes are coated with zinc to protect them from rusting.

Reason (R): Zinc is highly reactive with atmospheric oxygen. a.

Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A)

b. Both Assertion (A) and Reason (R) are true, and Reason(R) is not the correct explanation of Assertion (A) c. Assertion (A) is true, but Reasoning (R) is false d. Both Assertion (A) and Reasoning (R) are false 6. An electrolyte, when dissolved in water: a. Produces oppositely charged ions

b. Produces cations and anions

c. Produces only cations

d. Both a and b

7. To get the fine coating on an object in electroplating a. The surface of the object should be rough and free from greasy matter b. The concentration of electrolytes should be so adjusted c. Current must be the same throughout d. All of the above.

8. Iron is often electroplated because: a. Iron does not have a good appearance b. Iron is easily corroded by atmospheric air, humidity, and CO2 c. To make iron attractive d. All of the above 9. Electroplating is based on the: a. Magnetic effect of electricity

b. Chemical effect of electricity

c. Heating effect of electricity

d. Physical effect of electricity

10. During electroplating, the electrolyte solution must contain the ____________ of its compound. a. Metal

b. Non-metal

c. Salt

d. None of these

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CHEMICAL EFFECTS OF ELECTRIC CURRENT

WORKSHEET - 2 I.

MULTIPLE CHOICE QUESTIONS WITH SINGLE CORRECT ANSWER

1. An electrolyte a. Has a positive charge b. Has a negative charge c. Should be able to conduct charge without dissociating d. Should be able to form positive and negative ions 2. The full form of LED is a. Light emitting diode

b. Layer emission diode

c. Light emission diode

d. None of these

3. The electrolyte in the dry cell is a. Copper sulphate

b. Zinc sulphate

c. Sulphuric acid

d. Ammonium chloride

4. Liquids that conduct electricity are the solution of a. Acids

b. Bases

c. Salts

d. All of these

5. The terminal which is connected to a positive terminal of a battery is called a. Anode

b. Cathode

c. Neutral

d. None of these

6. To protect iron from surface corrosion and rust, it is coated with a. Tin

b. Zinc

c. Copper

d. Gold

7. During electrolysis, the sulphate ions move toward a. Any electrode

b. Battery

c. Electrolyte

d. Zinc electrode

8. Which of the following liquids does not conduct electricity? a. Lemon juice

b. Copper sulphate solution

c. Distilled water

d. Sugar solution

9. Which of the following objects is not electroplated with chromium?

94

a. Tap

b. Handlebar of bicycle

c. Table

d. Rim

IL Foundation Series Class 8

10. An anode is: a. A positively charged electrode b. A negatively charged electrode c. A wire used to connect the electrodes d. An electrolyte, which conducts electricity 11. A cathode is a: a. Positively charged electrode b. Negatively charged electrode c. Positively charged ion formed in the electrolyte d. Negatively charged ion formed in the electrolyte 12. A copper electrode during electrolysis: a. Donates electrons to hydrogen ions b. Accepts electrons from hydrogen ions c. Donates electrons to sulphate ions d. Accepts electrons from sulphate ions 13. During the electrolysis of copper sulphate, copper ions move towards: a. Anode

b. Cathode

c. Bottom

d. Remain stationary

14. Which of the following statements is true? a. During electrolysis, charge flows through the electrolyte solution via electrons b. The randomly moving electrons in a metal wire will start moving in a particular direction when a potential difference is applied across it c. A negatively charged particle has higher electric potential than a positively charged particle d. Charge flows only through negative charge carriers like electrons 15. Which of the following is a correct statement? a. All liquids conduct electricity b. Aluminium is an insulator c. All solids conduct electricity d. Sea water is a good conductor of electricity 16. The chemical reaction due to the passage of electric current depends on: a. Electrodes

b. Magnitude of current

c. Nature of electrolyte

d. All of these 95

CHEMICAL EFFECTS OF ELECTRIC CURRENT

17. Adding common salt to distilled water makes it a. Good conductor

b. Insulator

c. Can’t say

d. None of these

18. The principle of electrolysis is used in a. Extraction of metals

b. Purification of metals

c. Electroplating

d. All of these

19. On electrolysis, water splits into a. Positively charged hydrogen ions and negatively charged oxygen ions b. Negatively charged hydrogen ions and positively charged oxygen ions c. Hydrogen and oxygen atoms have positive and negative charges, respectively d. Hydrogen and oxygen atoms having negative and positive charges, respectively 20. The bulb does not glow when the probes are hung in the air. The reason is a. Air absorbs the electricity b. Air is a bad conductor of electricity c. Electricity is discharged into the air d. Air disperses the electricity 21. ____________ present in lemon juice acts as an electrolyte. a. Sulphuric acid

b. Nitric acid

c. Hydrochloric acid

d. Citric acid

22. When an electric current is flown through a conductor, some amount of a. Electrical energy is converted into heat energy b. Electrical energy is converted into mechanical energy c. Mechanical energy is converted into electrical energy d. Heat energy is converted into electrical energy 23. When current is passed through sodium chloride: a. Sodium is deposited at the positive electrode, and chlorine gas is formed at the negative electrode b. Sodium is evaporated, and chloride ions are formed at the negative electrode c. Sodium is deposited at the positive electrode, and chlorine is deposited at the negative electrode d. Sodium is deposited at the negative electrode, and the chlorine gas is formed at the positive

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IL Foundation Series Class 8

24. In the process of electrolysis a. Positive ions move toward the positive electrode, and negative ions move towards the negative electrode b. Positive ions move towards the negative electrode, and negative ions move towards the positive electrode c. Both ions move towards both electrodes in equal amounts until they are balanced d. None of the above 25. Electric current is the flow of particles with: a. A negative charge b. A positive charge c. Both positive and negative charges flowing opposite to each other d. Neutral charge 26. Which one of the following pairings is incorrect? a. Insulator–pure water

b. Conductor–copper wire

c. Electroplating–prevents rusting

d. None of these

27. Assertion (A): Some liquids are good conductors of electricity.

Reason (R): Liquids conduct electricity due to the flow of ions. a.

Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A)

b. Both Assertion (A) and Reason (R) are true, and Reason(R) is not the correct explanation of Assertion (A) c. Assertion (A) is true, but Reasoning (R) is false d. Both Assertion (A) and Reasoning (R) are false 28. Assertion (A): When electric current passes through copper sulphate solution, it dissociates into copper and sulphate ions.

Reason (R): Copper is a good conductor of electricity. a.

Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A)

b. Both Assertion (A) and Reason (R) are true, and Reason(R) is not the correct explanation of Assertion (A) c. Assertion (A) is true, but Reasoning (R) is false d. Both Assertion (A) and Reasoning (R) are false

97

CHEMICAL EFFECTS OF ELECTRIC CURRENT

29. Assertion (A): Insulators do not allow the flow of current through them.

Reason (R): Insulators have no free charge carrier. a.

Both Assertion (A) and Reason (R) are true, and Reason (R) is the correct explanation of Assertion (A)

b. Both Assertion (A) and Reason (R) are true, and Reason(R) is not the correct explanation of Assertion (A) c. Assertion (A) is true, but Reasoning (R) is false d. Both Assertion (A) and Reasoning (R) are false 30. Match the options of Column-I with Column-II. Column - I

98

Column - II

(A) Anode

1. Positively or negatively charged

(B) Cathode

2. Positive terminal

(C) Ions

3. Negative terminal

(D) Electrolyte

4. Conducting solution

a. A-2, B-3, C-1, D-4

b. A-3, B-4, C-2, D-1

c. A-1, B-3, C-4, D-2

d. A-4, B-2, C-1, D-3

5

5.1

SOME NATURAL PHENOMENA

HISTORY OF LIGHTNING

Lightning is a natural phenomenon characterised by the occurrence of electric sparks on a significant scale. In the past, the cause of these sparks was not understood, leading to fear and attributions to the wrath of gods. However, modern science explains that lightning is caused by the accumulation of electric charges in clouds.

5.1.1 Spark A spark is a sudden, visible electrical discharge that occurs when there is a breakdown in the dielectric strength of the air or another insulating medium. This breakdown allows the flow of electric current, creating a brief, visible flash of light. Sparks can be generated intentionally, such as in electrical equipment like spark plugs, or unintentionally in everyday situations, such as when static electricity builds up and discharges.

5.1.2 Lightning Lightning is a natural and powerful form of electrical discharge that occurs in the sky during thunderstorms. It is caused by the accumulation of electrical charges in the atmosphere, particularly in clouds. When the charge difference becomes too great, it results in a rapid discharge of electricity in the form of a lightning bolt. Lightning is often accompanied by thunder, which is the sound produced by the rapid expansion and contraction of air surrounding the lightning channel.

Lightning can occur between clouds, within a cloud, or between a cloud and the ground, and it is a common meteorological phenomenon. Lighting can be hazardous and requires precautions for safety.

Fig. 5.1 Lightning

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SOME NATURAL PHENOMENA

5.2 METHODS OF CHARGING 5.2.1 Charging by rubbing When a plastic refill is rubbed with polythene or a plastic comb is rubbed with dry hair, they both acquire a small electric charge. These objects are referred to as charged objects. During the charging process, polythene and hair also get charged. Here, the rubbing of a plastic refill with polythene or a plastic comb with dry hair results in the acquisition of electric charges by both the objects involved in the rubbing process.

Objects Rubbed

Materials Used for Rubbing

Attracts/Does Not Attract Pieces of Paper

Charged/Not Charged

Refill

Polythene, woollen cloth

Attracts

Charged

Balloon

Polythene, woollen cloth, dry hair

Attracts

Charged

Eraser

Wool

Attracts

Charged

Steel spoon

Polythene, woollen cloth

Does Not Attracts

Not Charged

Table 5.1 Charging of objects when rubbed with other objects

5.2.2 Charging by conduction and induction Charging by conduction occurs when a charged particle comes into direct contact with a neutral conductor. During this process, charges from the particle are transferred directly to the conductor, leading to the conductor acquiring the same charge as the charged particle.

On the other hand, charging by induction involves charging a neutral conductor without direct contact with a charged particle. Instead, a charged particle is brought close to the conductor, nearly touching it, while the conductor remains grounded. This proximity causes a transfer of charge between the particle and the conductor, resulting in the conductor acquiring a charge opposite in polarity to that of the charged particle.

5.3 TYPES OF CHARGES AND THEIR INTERACTION Charge is the property of matter which can be produced and affects the electric and magnetic fields.

Charges are of two types: Negative charges and positive charges.

When a glass rod is rubbed with silk cloth, conventionally the charge acquired by a glass rod is called a positive charge, and the charge acquired by the silk cloth is a negative charge. Similarly, when an ebonite rod, a type of hard rubber, is rubbed with wool, electrons transfer from the wool to the ebonite, giving the ebonite a negative charge.

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Electrons Negative Charge

Protons

Positive Charge

Electric Fig. 5.2 Charge Electric charge 5.3.1 Positive and negative charges Positive Charges: Positive charges are a fundamental concept in electricity, representing an excess of protons in an object.

Negative Charges: Negative charges, on the other hand, indicate an excess of electrons in an object.

5.3.2 Interaction between charges • Similarly charged bodies repel each other, and oppositely charged bodies attract to each other.

• A charged balloon repels another charged balloon.

• A charged refill repels another charged refill.

• A charged balloon attracts a charged refill.

• When a glass rod is rubbed with silk, electrons are transferred from the glass to the silk, leaving the glass rod positively charged and the silk negatively charged.

• When a charged glass rod is brought near a charged plastic straw (rubbed with polythene), there is an attraction between them.

• The plastic straw is inferred to carry a negative charge.

Nature of Electrical Charges

The charges generated by rubbing are static, meaning they do not move by themselves.

The motion of charges constitutes an electric current observed in circuits that power bulbs or heat wires.

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5.4 TRANSFER OF CHARGE The transfer of charge refers to the movement of electric charge from one object to another. This phenomenon is commonly observed in various natural occurrences and is crucial in understanding how electricity behaves.

5.4.1 Electroscope An electroscope is an instrument used to detect the presence and nature of electric charge on an object. It consists of a metal rod or stem attached to a metal disc and two thin metal foil strips at the bottom. The metal stem is insulated from the surroundings using a non-conductive material.

The following figure shows a simple electroscope.

Brass Disc

Insulator plug Brass rod Glass bottle Gold leaves

Metal Foil

Earth

Fig. 5.3 Electroscope Parts of an Electroscope: An electroscope is made from metals like gold, silver, copper, or aluminium because they conduct electricity well.

It's like a glass jar with a metal rod sticking out of a cork. At one end of the rod, there's a metal disc or rod, and at the other end, there are two thin gold leaves hanging down. They move when electricity is present.

Working of an Electroscope: Initially, the electroscope is in a neutral state, meaning it has an equal

number of positive and negative charges. When the metal disc is touched with a charged body, aluminium strips move away from each other. This happens because some of the charges of the body charges are transferred to the strips through the metal rod. This method of charging a body is called charging by conduction. The nature of charges on both the leaves and the charged body are similar. Hence, both the leaves of the aluminium foil/gold foil will move away from each other. If the body was not charged, then the leaves of the foil would remain as they were before. They would not repel each other.

Charge Detection: The divergence of the metal strips serves as an indicator of the presence and

nature of the charge. The greater the divergence, the higher the charge on the electroscope.

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Discharge: If the end of the metal stem is touched, the excess charge is transferred to the earth,

neutralizing the electroscope. This process is called discharge. The discharge process allows the electroscope to return to a neutral state after being charged.

Earthing: Earthing involves providing a pathway for excess charge to flow into or out of the earth. In

the case of an electroscope, touching the metal stem accomplishes this and brings the electroscope back to a neutral state.

An electroscope is a simple yet effective device for detecting and studying electric charges.

5.4.2 Earthing In an electroscope, when the foil strips are charged and touched with a hand, they collapse, indicating a discharge. This phenomenon occurs because the foil strips lose charge to the earth through the person's body. This process is known as earthing.

Earthing is a crucial safety measure implemented in buildings to shield individuals from potential electrical shocks resulting from any inadvertent leakage of electrical current. This protective mechanism ensures that any excess electricity is safely directed into the ground, preventing harm to occupants and minimizing the risk of accidents.

In daily life, the grounding of electrical appliances and installations, such as power outlets and electrical panels, exemplifies the practical application of earthing. This precautionary measure plays a pivotal role in maintaining a safe environment by redirecting electrical currents away from individuals and minimizing the possibility of electric shocks.

5.5 THE STORY OF LIGHTNING During the development of a thunderstorm, vigorous movements of air currents upward and water droplets downward lead to the separation of charges. In the process, positive charges gather near the upper edges of clouds, negative charges accumulate near the lower edges, and positive charges also accumulate near the ground. When the accumulated charges reach a critical magnitude, the + + + ++ + + + normally poor conductor, air, can no longer resist their flow. This leads to the meeting of negative - - - - - - -- and positive charges, resulting in streaks of bright - - -light and sound, observed as lightning. The overall phenomenon is termed an electric discharge. The process of electric discharge can occur between two or more clouds or between clouds and the earth.

+++++++++ Fig. 5.4 Accumulation of charges leading to lightning

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5.6

SAFETY PRECAUTIONS DURING LIGHTNING AND THUNDERSTORM

Protective measures against lightning/thunderstorms are as follows: i. Stay or go indoors. If you hear thunder, do not go outside unless absolutely necessary. ii. Stay away from anything that could conduct electricity. iii. Do not touch any electric wires, telephone cables, metal pipes, etc. iv. Do not hold an umbrella during lightning. Charges may pass through the metallic rod of the umbrella to the person carrying it.

Fig. 5.5 Safety precautions during lightning and thunderstorm

v. Do not stay in an open place such as an open vehicle like a motorbike, tractor, open fields, elevated places, or tall trees. vi. Do not come in contact with the running water. vii. Unplug all the electrical appliances in the house, for example, TVs, computers or music systems.

5.6.1 Lightning conductors A lightning conductor serves as a protective measure for buildings against the potential impact of lightning. Typically, it involves installing a tall metallic rod, taller than the building itself, into the walls during construction. One end of the rod extends into the air, while the other is securely buried in the ground so that charges are directly transferred to the earth by the rod (Earthing).

This design facilitates a straightforward pathway for the transfer of electric charge to the ground, minimizing the risk of damage caused by lightning strikes. Additionally, various metal elements

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in buildings, such as columns, electrical wires, and water pipes, contribute to protection. However, caution is advised against touching these elements during a thunderstorm.

Fig. 5.6 Lightning rod

What should we do when someone is struck by lightning?

We should try to give possible first aid to the lightning victims, as they may need artificial respiration. Mouth breathing is an easy way of providing artificial breathing. The lightning victim should immediately be taken to hospital as burning injuries or other internal injuries may prove fatal.

5.7 EARTHQUAKES 5.7.1 What is an earthquake?

An earthquake is a sudden shaking or trembling of the earth that occurs for a brief duration. It results from a disturbance deep within the earth's crust, causing seismic activity. While minor earthquakes happen frequently worldwide and go unnoticed, major ones can lead to significant damage to structures, bridges, dams, and human lives.

Earthquakes can cause:

1. Loss of life 2. Loss of property such as buildings, bridges and dams 3. Flood, landslide, or tsunami

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Fig. 5.7 Loss of property due to earthquake

5.7.2 Causes of earthquakes Earthquakes are primarily caused by disturbances in the uppermost layer of the earth, known as the crust. This layer is divided into fragments called plates, which are in constant motion. When these plates interact, whether colliding or brushing past each other, they create disturbances in the crust, manifesting as earthquakes. The movement of the earth's plates is a natural geological process, and the boundaries of these plates, termed seismic or fault zones, are vulnerable areas where earthquakes are more likely to occur.

In India, the areas facing higher earthquake risks encompass Kashmir, the Western and Central Himalayas, the entire Northeast region, Rann of Kutch, Rajasthan, and the Indo-Gangetic Plain.

Additionally, certain parts of South India are also within the danger zone.

5.7.3 Measurement of power of an earthquake The intensity of an earthquake is quantified using the Richter scale, which expresses the magnitude of the seismic event. Destructive earthquakes typically register a magnitude higher than 7 on the Richter scale. The scale helps gauge the power and potential impact of an earthquake. India experienced a significant earthquake on 8 October, 2005, affecting Uri and Tangdhar towns in northern part of Jammu and Kashmir. Additionally, a major earthquake struck Bhuj district in Gujarat on 26 January, 2001. Both had magnitudes higher than 7.5 on the Richter scale.

5.7.4 Protection against earthquakes Despite advances in understanding the causes of earthquakes, predicting when and where they will occur remains challenging. Certain regions are more prone to earthquakes due to their proximity to plate boundaries, known as seismic zones, or fault lines. Utilising modern building technology and 106

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consulting qualified architects and structural engineers can contribute to creating structures that are 'Quake Safe.'

Securing furniture and belongings within the building is essential. Fixed cupboards and shelves on walls prevent easy toppling, minimising the risk of injury during an earthquake. Strategic placement of items like wall clocks, photo frames, and water heaters should be considered to avoid potential hazards. Given the risk of fires triggered by earthquakes, it's crucial for all buildings, especially tall structures, to be equipped with functional firefighting equipment.

The Central Building Research Institute in Roorkee has developed expertise in constructing earthquake-resistant houses. In the unfortunate event of an earthquake, certain protective measures can be taken: If at home

Seek shelter under a table and remain there until the shaking subsides.

Keep a safe distance from tall and heavy objects that could fall.

If in bed, avoid getting up; protect your head with a pillow.

If outdoors

Locate an open area away from buildings, trees, and overhead power lines. Drop to the ground.

If in a car or bus, remain inside. Instruct the driver to drive slowly to a clear area and avoid disembarking until tremors cease.

5.7.5 Seismograph To monitor and measure seismic activity, scientists use a seismograph, an instrument designed to record and analyze ground vibrations. This helps in studying earthquake patterns, understanding their behaviour, and contributing to better preparedness and response strategies. While scientific knowledge about earthquakes has advanced, predicting these natural phenomena with precision remains an ongoing challenge.

Frame Wire

Weight Rotating drum

Vibrations

Base

Fig. 5.8 Seismograph

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QUICK REVIEW • When a glass rod is rubbed with a silk piece, it gets a positive charge, and the silk piece develops an equal amount of negative charge.

• When an uncharged body is touched by another charged body, it acquires a similar charge by 'conduction'.

• An electroscope is used to detect, measure, and find the nature of charge.

• The process of transferring charge from a charged object to the earth is called earthing.

• Lightning and thunder are caused when clouds get charged during a storm.

• A rapid flow of charge through the air in between two oppositely charged clouds is called lightning.

• Open fields, tall trees, shelters in parks, and elevated places do not protect us from lightning strokes. Carrying an umbrella is not at all a good idea during thunderstorms.

• Electrical appliances like computers, TVs, etc., should be unplugged. Electrical lights can remain on.

• A loud noise followed by a flash of lightning is called thunder.

• Lightning conductors are installed in very tall buildings to protect them against lighting.

• An earthquake is caused by the shaking of the ground by the sudden movements in the earth's crust.

• Two major earthquakes occurred in India on 8 October 2005 in Jammu and Kashmir and on 26 January 2001 in Gujrat.

• The magnitude of an earthquake is measured on the Richter scale.

• Tremors on the earth can also be caused when a volcano erupts.

• Seismic waves are the waves generated by an earthquake. Seismic movements are monitored and measured by an instrument called seismograph.

• Earthquakes can cause tremendous damage. The damage can be reduced by adopting some protection against earthquakes.

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WORKSHEET - 1 MULTIPLE CHOICE QUESTIONS WITH SINGLE CORRECT ANSWER I. History of lightning and methods of charging

1. Which of the following cannot be charged easily by friction? a. Glass rod

b. Ball of wool

c. Copper rod

d. Inflated balloon

2. Lightning is the process of a. Producing positive charges

b. Detecting negative charges

c. Electric discharge

d. None of the above

3. When a glass rod is rubbed with a silk cloth, then the silk cloth gets a. Negatively charged

b. Positively charged

c. Both positively and negatively charged

d. Remains neutral

4. Due to the motion of a charge, its magnitude a. Changes

b. Does not change

c. Increases or decreases depending on its speed

d. Cannot be predicted

5. To know the presence of a charge on a body a. Attraction is sometimes a sure test

b. Repulsion is a sure test

c. Attraction is a sure test

d. Both a and b

II. Types of charges and transfer of charge

1. If a charged body attracts another body, then the charge on the other body a. Must be positive

b. Must be negative

c. Must be zero

d. May be positive, negative, or zero.

2. Unlike charges a. always attract each other

b. always repel each other

c. can attract or repel, depending on conditions

d. neither attract nor repel each other

3. Induction precedes attraction because a. An uncharged body can attract an uncharged body due to induction of the opposite charge on it b. A charged body can attract an uncharged body due to induction of some charge on it c. A charged body can attract an uncharged body due to induction of opposite charge on it d. A charged body can attract another charged body due to induction of same charge on it 109

SOME NATURAL PHENOMENA

4. When charge is given to a body a. More charge accumulates at regions of small curvature b. More charge accumulates at regions of large curvature c. Charge is distributed uniformly irrespective of curvature d. None of the above is true 5. When a body is connected to the earth, electrons from Earth flow into the body. This means the body initially is a. Uncharged

b. Charged positively

c. Charged negatively

d. An insulator

6. Assertion (A): Like charges repel each other.

Reason (R): Unlike charges attract each other. a. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A) b. Both Assertion (A) and Reason (R) are true and Reason(R) is not the correct explanation of Assertion (A) c. Assertion (A) is true, but Reasoning (R) is false d. Both Assertion (A) and Reasoning (R) are false 7. Which of the following cannot be charged easily by friction? a. A plastic scale

b. A copper rod

c. An inflated balloon

d. A woollen cloth

8. When a glass rod is rubbed with a piece of silk cloth the rod a. And the cloth both acquire positive charge b. Becomes positively charged while the cloth has a negative charge c. And the cloth both acquire negative charge d. Becomes negatively charged while the cloth has a positive charge 9. The charges produced on same type of objects rubbed by the same material are a. Similar or like charges

b. Unlike or dissimilar charges

c. Neutral

d. None of these

10. When a charged body is brought closer to an uncharged body, then a. The charged body attracts an uncharged body b. The charged body induces an opposite charge on uncharged body c. The charged body repels the uncharged body d. Both a & b

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III. Safety precautions during lightning and thunderstorms

1. The process of discharging atmospheric electricity into the earth by a lightning conductor is called a. Short circuiting

b. Electrical neutralization

c. Earthing

d. Both a and b

2. A lightning conductor is a a. Substance that can be charged by clouds. b. Copper plate buried in the ground. c. Metal rod with spikes, ending in a copper plate buried in the ground, fixed to a building. d. Piece of wire through which current can flow.

3. During the development of a thunderstorm a. There will be fast movement of air currents b. The clouds moving in air acquire a charge on their surface due to friction with particles of air c. Discharge takes place between oppositely charged clouds d. All the above 4. The accumulated charge on the clouds always tries to discharge in the form of lightning through a. A hill or tower which is several miles away from it

b. An object that it selects

c. The tallest object within about 50 yards radius

d. All the above

5. A lightning conductor consists of a. Long, thick metal rod or strip

b. Blunt edge at its upper-end

c. Sharp spikes at its upper-end

d. Both a and c

6. Assertion (A): Lightning conductors can protect a building from lightning.

Reason (R): Because the earth is not a huge absorber of electricity. a. Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A) b. Both Assertion (A) and Reason (R) are true and Reason(R) is not the correct explanation of Assertion (A) c. Assertion (A) is true, but Reasoning (R) is false d. Both Assertion (A) and Reasoning (R) are false 7. To protect us from electric shocks caused by any leakage of electrical charge, in buildings a. Electric insulation is provided

b. Earthing is provided

c. Charge repellers are provided

d. All of the above

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IV. Earthquakes

1. The magnitude of earthquakes is measured in which scale? a. Richter scale

b. Earthquake meter

c. Newton scale

d. Galileo's scale

2. Sudden shaking of the earth is called a. Lightning

b. Thunderstorm

c. Earthquake

d. Landslide

3. The point at which the earthquake originates is known as a. Mantle

b. Seismic focus

c. Surface wave

d. Body wave

WORKSHEET - 2 MULTIPLE CHOICE QUESTIONS WITH SINGLE CORRECT ANSWER 1. When a highly charged cloud passes over a tall building then a. It induces an opposite charge on the spikes of the lightning conductor b. It induces an opposite charge on the surface of building c. Induced charge quickly flows to the earth through the conductor d. Both a and c 2. Lightning strikes produced during a thunderstorm a. Can destroy the life and property b. Can help in fixation of atmospheric nitrogen c. Can help in the formation of ozone from atmospheric oxygen d. All the above 3. The movement in the earth's crust is due to a. Energy released from the core of the earth due to radioactive decay b. Gravitational influence of the moon c. Gravitational influence of mars d. Energy released by the ocean during continuous thrust on land mass 4. To measure an earthquake seismologists use the devices a. Seismoscope

b. Seismometer

c. Seismograph

d. All the above

c. Equal to 7

d. None of these

5. The destructive earthquakes have magnitudes a. Lower than 7

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6. Richter scale ranges from a. 0 to 7

b. 0 to 9

c. 0 to 12

d. 0 to 6

7. On Richter scale, an increase of 2 in magnitude means a. 100 times more destructive energy

b. 10 times more destructive energy

c. 1000 times more destructive energy

d. None of these

8. Which of the following countries in the world is most prone to earthquakes? a. China

b. Japan

c. India

d. Russia

c. Gujarat

d. Kerala

9. The state most prone to earthquakes in India is a. Chhattisgarh

b. Tamil Nadu

10. A gold leaf electroscope can be used a. Only to detect a charge

b. Only to find the nature of a charge

c. Only to measure a charge

d. To detect, compare, and find the nature of a charge

11. The person who proved that lightning and the spark from your clothes are essentially the same phenomenon was a. Gilbert

b. Sir Humphry Davy

c. Benjamin Franklin

d. Michael Faraday

12. Which of the following statements is correct? a. Positive charges only repel negative charges, while negative charges attract positive charges. b. Positive charges attract both positive and negative charges, while negative charges only repel positive charges. c. Positive charges attract negative charges, while negative charges attract positive charges. d. Positive charges repel each other, while negative charges attract each other.

13. Object A and B repel each other but attract C. C repels D. If D is positively charged then the charge on B is a. The charge on object B cannot be determined from the given information b. Object B is uncharged c. Object B is positively charged d. Object B is negatively charged 14. Which of the following statements is correct? a. In conduction, the conductor is touched by the charged body while in induction, the charged body is brought near the conductor. b. In both conduction and induction, bodies need not be in contact.

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c. Charge is not transferred in both conduction and induction. d. In both conduction and induction phenomena the bodies need to be in contact.

15. Which of the following statements is true? a. Static electricity and current electricity are both induced in insulator surfaces b. Static electricity and current electricity are both induced in electric conductors c. Static electricity is induced in electric conductors, while current electricity flows in insulator surfaces d. Static electricity is induced in insulator surfaces, while current electricity flows in electric conductors 16. Which of the following does not come under the safety measures for lightning? a. Avoid standing near tall objects or structures b. Seek shelter in a fully enclosed building c. Use electrical equipment such as phones and computers d. Avoid open fields, high ground, or bodies of water during a storm 17. When the ebonite rod is rubbed with a woollen cloth, then the ebonite rod becomes a. No charge

b. Positively charged

c. Negatively charged

d. Can be negative or positive

18. Which of the following statements is true? a. The movement of plates has no relation to earthquakes b. Weak zones are called Seismic Zones c. The location where earthquakes occur is called a plate boundary d. Earthquakes are caused by volcanic eruptions 19. A lightning strike is made up of multiple fast flashes, how long does each flash last? a. About a millisecond b. About 1/10 of a second c. About 1/100 of a second d. About 1 second 20. Ram has 3 charged objects, namely A, B, and C. When he brings object A close to object B, they repel each other. When he brings object B close to object C, they attract each other.

Which of the following options can be true for the objects? a. The charges on the objects are: A - Positive, B - Negative, and C - Negative b. The charges on the objects are: A - Positive, B - Positive, and C - Negative c. The charges on the objects are: A - Positive, B - Negative, and C - Positive d. The charges on the objects are: A - Positive, B - Positive, and C - Positive 114

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21. If air and clouds were good conductors of electricity, do you think lightning could occur? a. No, because charge separation cannot take place in the conductor b. No, because charge separation can take place in the conductor c. Yes, because charge combines in the conductor d. Yes, because charges can nullify 22. Which of the following statements accurately describes the function and operation of an electroscope? a. An electroscope is a device that measures the temperature of an object b. An electroscope is a device that detects the presence and polarity of electric charges in a body c. An electroscope is a device that detects the presence and magnitude of magnetic fields d. An electroscope is a device that measures the intensity of electric currents in a circuit 23. When two uncharged dry objects, A and B, are rubbed against each other, which of the following can possibly happen? a. A and B acquire equal and similar charges

b. Earthing is provided charges

c. A and B acquire unequal and similar charges

d A and B acquire unequal and opposite

24. Under what condition does the electric discharge occur? a. When there is no source of electricity b. When two bodies with the same electric potential are connected c. When a single body is isolated and not connected to any other object d. When two bodies with different electric potentials are connected 25. A major earthquake occurred in India on 8 October 2005. Which place among the following was affected? a. Assam

b. Karnataka

c. Gujarat

d. Jammu and Kashmir

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6

LIGHT

6.1 WHAT MAKES THINGS VISIBLE? The eyes cannot see objects on their own, especially in the dark. The ability to see objects relies on the light entering our eyes, either emitted or reflected by an object.

6.1.1 Light Light is a form of energy that causes the sensation of sight. A substance through which light can pass, more or less, is known as an optical medium. There are three different types of media: 1. Transparent: It is the medium through which light can easily pass. Here, the light is not absorbed at all or is very minimally absorbed.

E.g., air, thin glass, clear water of shallow depth, etc.

2. Translucent: It is the medium through which light can partially pass, but things cannot be clearly seen. Here, the light is absorbed to a great extent.

E.g., ground glass, tracing paper, etc.

3. Opaque: It is the medium through which light cannot pass.

E.g., wood, stone, etc.

6.2 BEAM OF LIGHT The path along which the light energy travels is called the ray of light. Light rays that are very near to each other, when taken together, constitute a beam of light.

6.2.1 Types of beams of light 1. Parallel beams of light: These rays are parallel to each other.

Fig. 6.1 A parallel beam of light

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2. Convergent beam of light: These light rays proceed to a point from different directions.

Fig. 6.2 A convergent beam of light

3. Divergent beam of light: These light rays spread in different directions from a point.

Fig. 6.3 A divergent beam of light

6.3 REFLECTION OF LIGHT In a homogeneous medium, light travels in a straight line, but when it falls on another medium, it suffers the following changes: • A portion of the light is absorbed.

• A portion of the light is turned back into the first medium in a definite direction.

• The remaining portion of light enters the second medium, provided the medium is transparent and light travels in a different path.

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6.3.1 Reflection Light comes back into the same medium when it encounters a boundary separating the two media.

This is called reflection. The surface from which reflection takes place is called a reflector.

Terms related to the reflection of light

• Incident ray: The incoming ray of light that strikes a surface or boundary separating any two media. It represents the path of light before it encounters the surface.

• Reflected ray: The outgoing ray of light that results from the reflection of the incident ray off a surface. It represents the path of light after it has bounced off the surface.

• Normal line: The line drawn perpendicular to the surface of the medium at the point of incidence or reflection.

• Angle of incidence: The angle made by the incident ray with the normal to the surface is called the angle of incidence.

• Angle of reflection: The angle made by the reflected ray with the normal to the surface is called the angle of reflection.

6.3.2 Laws of reflection There are two laws of reflection: 1. First law: The incident ray AO, the normal NO to the reflecting surface at the point of incidence O, and the reflected ray OB all lie in the same plane.

2. Second law: The angle of incidence (i) is equal to the angle of reflection (r).

N

A

α

B

i r d O

Fig. 6.4 Reflection of light

Also, note that in the diagram, α is the glancing angle, and d is the angle of deviation.

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Glancing angle: The angle made by the incident ray with the surface is called the glancing angle (α).

Angle of deviation: The angle made by the extended incident ray with the reflected ray is called the angle of deviation (d).

From the figure 6.4, i + r + d = 180 d = 180 - (i + r)) We know that: i=r d = 180 - 2i (or) 180 - 2r

SOLVED EXAMPLES Example 1: An incident ray makes an angle of 35° with the surface of a plane mirror. What is the angle of reflection?

Solution: I n order to find the angle of reflection, we should first know the angle of incidence. In this case, the incident ray makes an angle of 35° with the surface of the mirror (from the figure).

So, the angle of incidence = 90°-35° = 55°.

Since the angle of incidence is 55°.

Therefore, the angle of reflection is also 55°. plane mirror M

A i

angle of incidence N angle of reflection

35° 55°

O

55°

r

B

M’

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Example 2: What is the angle of incidence of a ray if the reflected ray is at an angle of 90° to the incident ray?

Solution: According to the law of reflection, the angle of incidence is equal to the angle of reflection. It is given that the angle between the incident ray and the reflected ray is 90°. ⇒∠i+∠r = 90° ⇒∠i+∠i = 90° ⇒2∠i = 90°

⇒∠i = 90°/2 = 45°

6.4 TYPES OF REFLECTION Reflection of light can be categorised into two types: regular reflection and diffused reflection.

6.4.1 Regular reflection When reflection takes place on a perfectly smooth plane surface, then the reflection is called regular reflection.

In this case, a parallel beam of light incident on the surface will remain parallel even after the reflection, as shown in the figure.

Fig. 6.5 Regular reflection

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In the case of regular reflection, the reflected light ray has a large intensity in one direction and a negligibly small intensity in other directions. Regular reflection of light is useful in determining the properties of a mirror.

6.4.2 Diffused reflection If the reflecting surface is rough (or uneven), a parallel beam of light is reflected in random directions. This kind of reflection is called diffused reflection.

As shown in Figure 6.6, if the reflecting surface is rough, the normal at different points will be in different directions. Thus, the rays that are parallel before the reflection will be reflected in random directions.

Fig. 6.6 Diffused reflection

6.5 REFLECTION ON PLANE MIRROR The reflection of light is observed on a plane or on curved surfaces.

Note: The basic laws of reflection are the same for plane and curved surfaces. The point of intersection of the incident rays is called an object, and the point of intersection of the corresponding reflected rays is called its image.

The images are of two types: virtual and real.

6.5.1 Types of images 1) Real image: A real image is formed when light rays converge at a specific point after reflecting from the surface. For example, images obtained on a TV screen.

2) Virtual image: A virtual image is formed when light rays seem to converge at a point behind the surface after reflecting from the surface. For example, images formed on a mirror.

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N N I real image

O virtual object O object

N

I image

(a) Real image (b) Virtual image Fig. 6.7 Types of images Characteristics of the image of a real object formed due to the reflection by a plane mirror

• If the object is real, then the image formed by a plane mirror is virtual, erect, of the same size, and at the same distance from the mirror.

• Magnification of a plane mirror is m =

Size of the image Size of the object

Lateral Inversion: The phenomenon where the left and right sides of an object or image appear switched or reversed when viewed through a mirror or in a reflection. This effect is a characteristic feature of plane mirrors and contributes to our perception of reflected images.

Fig. 6.8 Lateral inversion

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6.6 MULTIPLE REFLECTIONS OF LIGHT Multiple reflections of light refers to the phenomenon in which light undergoes more than one reflection before reaching an observer. This can occur when light reflects off multiple surfaces or mirrors successively. Each reflection alters the direction of light, and the cumulative effect can lead to interesting visual outcomes.

Number of images between two plane mirrors

If two plane mirrors are kept at an angle θ to each other, the number of images of a point object kept between the two mirrors is given as follows: If the position of the object is asymmetrical with respect to the two mirrors, then: n= =

2π θ

-1

2π

(if

2π θ

is even)

(otherwise)

θ

If the position of the object is symmetrical with respect to the two mirrors, then, n=

2π θ

-1.

Example: How many images of a candle will be formed if it is placed between two parallel plane mirrors separated by 40 cm?

Solution: When two mirrors are placed parallel to each other, then an infinite number of images are formed.

6.7 APPLICATION OF MULTIPLE REFLECTIONS OF LIGHT A kaleidoscope utilises the principle of multiple reflections of light.

Principle of multiple reflections: A kaleidoscope operates on the principle of multiple reflections of light. It consists of three main components: a source of light, mirrors, and a set of colourful objects (such as glass pieces or beads).

Reflections inside the kaleidoscope: When light from an external source enters the kaleidoscope, it reflects off the mirrors inside. The mirrors are arranged at specific angles to create multiple reflections of the colourful objects placed inside.

Creation of patterns: As light undergoes successive reflections, patterns are formed due to the symmetrical arrangement of mirrors. Each reflection contributes to the complexity of the pattern, creating a visually appealing and ever-changing image.

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LIGHT Cardboard tube Small hole Transparent glass disc

Cardboard disc

Ground glass disc

Three mirror strip

Small pieces of coloured glass

Fig 6.9 Kaleidoscope

Symmetry: The mirrors are usually arranged in a symmetrical fashion, resulting in symmetrical patterns in the kaleidoscope's view. The symmetry enhances the beauty of the patterns and makes the visual experience more captivating.

6.8 DISPERSION The splitting of white light into seven colours when passing through a prism is called dispersion.

The sequence of the seven colours comprises violet, indigo, blue, green, yellow, orange, and red, often remembered using the acronym VIBGYOR. This arrangement of colours is known as a spectrum. Each colour has a different wavelength, causing them to bend by different amounts as they pass through the medium.

it

Wh

ht

g e li

Glass prism Fig. 6.10 Dispersion of white light

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Red Orange Yellow Green Blue Indigo Violet

IL Foundation Series Class 8

6.8.1 Sunlight - white or coloured When sunlight, which appears white to our eyes, undergoes dispersion, it reveals its composite nature. Sunlight is a combination of various colours, each corresponding to a specific wavelength. As it passes through a medium like a prism, the different colours bend by different amounts.

This bending causes the colours to spread, creating a spectrum of colours. The result is a display of vibrant hues of the following colours: red, orange, yellow, green, blue, indigo, and violet. This phenomenon beautifully illustrates that what we perceive as white sunlight, in fact, is a mixture of diverse colours that become visible when subjected to the process of dispersion.

A rainbow is a natural spectrum appearing in the sky after a rain shower. It is caused by the dispersion of sunlight by tiny water droplets in the atmosphere. A rainbow is always formed in the direction opposite to that of the sun. The water droplets act like small prisms.

Fig. 6.11 Rainbow formation

6.9 THE HUMAN EYE The eyes are crucial sense organs for us. They help us sense the light entering our eyes, which enables our vision.

6.9.1 Structure of the human eye 1. Sclera: The outer protective layer of the eye, known as the sclera, is a tough, white covering that encases the eyeball.

2. Cornea: It is a transparent structure that is positioned at the front of the eye and allows light to enter the eye.

3. Iris: The iris is a ring-like, muscular structure positioned behind the cornea. It's responsible for the eye's colour and controls the size of the pupil.

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4. Pupil: The pupil is a small hole within the iris that regulates the amount of light entering the eye.

5. Lens: The lens, situated behind the pupil, is a transparent structure that adjusts its shape to focus light onto the retina, facilitated by the ciliary muscles.

6. Aqueous humour: This clear liquid fills the space between the cornea and eye lens, contributing to the eye's shape and nutrient needs.

7. Retina: The retina comprises light-sensitive nerve cells and converts light into electrical impulses, which are then transmitted through the optic nerves to the brain for interpretation.

8. Vitreous humour: The vitreous humour is a clear gel-like substance that fills the space between the eye lens and retina. It helps maintain the eye's shape and optical properties.

9. Optic Nerves: The optic nerves consist of two types of nerve cells: cones and rods. Cones are sensitive to bright light, while rods are sensitive to dim light.

10. Blind Spot: Located at the junction of the optic nerve and retina, the blind spot lacks sensory nerve cells, resulting in an area of no vision.

Sclera Retina Lens Iris Optic nerve Pupil Cornea Ciliary body and muscle Vitreous body

Blind spot

Fig. 6.12 Structure of the human eye Image persistence

• The visual impression of an image remains on the retina for approximately 1/16th of a second before fading. Consequently, if static images of a moving object are presented to the eye at a frequency exceeding 16 per second, the brain interprets the sequence as motion. Films, in essence, comprise numerous individual frames displayed sequentially. Typically, these frames are projected at a rate of 24 per second, surpassing the 16-per-second threshold, thereby creating the illusion of a continuous moving picture.

Eyelids

• In its design, nature has equipped eyes with eyelids to serve as protective barriers, preventing foreign objects from entering. Additionally, eyelids have the function of blocking out light when it is not needed.

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Minimum distance for clear vision

• The eye is an extraordinary instrument capable of clear vision both at a distance and up-close, under normal conditions. However, the minimum distance required for the eye to perceive objects distinctly varies with age. For a normal eye, the most comfortable distance for reading is approximately 25 cm.

6.9.2 Power of accommodation The eye lens, essential for vision, is composed of a flexible and jelly-like material. Ciliary muscles, which play a crucial role in vision, have the ability to modify the curvature of the eye lens.

When the ciliary muscles are in a relaxed state, the lens becomes thin, resulting in an increased focal length (the point where incoming light rays meet after passing through the eye lens). This phenomenon enhances clarity in viewing distant objects. Conversely, when the ciliary muscles contract, the lens thickens, altering its curvature and decreasing the focal length. This adjustment facilitates clear vision of nearby objects. The eye lens possesses the remarkable capability of adjusting its focal length, a phenomenon referred to as accommodation. However, there is a limitation to this adjustment, as the focal length cannot be decreased beyond a specific minimum limit. It is essential to note that holding objects too close to the eyes, challenging the minimum focal length, can result in blurred vision and eye strain.

6.10 EYE DEFECTS Distinct vision range: For optimal vision without strain, objects are seen most distinctly at the least distance of distinct vision, approximately 25 cm. This range accommodates the natural capabilities of the eye lens for clear and comfortable viewing.

Near point: The minimum distance for clear vision, also known as the near point, is approximately 25 cm for a young adult with normal vision.

Far point: The farthest point for clear vision is infinity for a normal eye.

Clear vision range: A normal eye can see objects clearly within the range of 25 cm to infinity.

Lenses: A lens is a transparent refracting medium bounded by two spherical surfaces.

Lenses are two types: 1. Convex lens and 2. Concave lens.

Concave

Convex

Fig. 6.13 Lenses

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Convex lens: A convex lens is thicker in the middle than at the edges. It is also known as a converging lens.

Concave lens: A concave lens is thinner at the centre than the edges. It is also known as a diverging lens.

6.10.1 Myopia (near-sightedness) Myopia is a vision condition where distant objects appear blurry while close objects are visible clearly.

There are two major causes of myopia. They are: i) Elongation of the eyeball. ii) Excessive curvature of the eye lens.

Correction of myopia: A concave lens of suitable focal length is used to correct a myopic eye.

O

(a) Far point of a myopic eye O’

O

(b) Myopic Eye

O

(c) Correction for myopia Fig. 6.14 Myopia

6.10.2 Hypermetropia (far-sightedness) Hypermetropia is a vision defect in which an eye can see distant objects clearly but can not see nearby objects distinctly.

• For a hypermetropic eye, the near point is farther away from a normal near point (25 cm).

• For this defective eye, the image of an object is formed behind the retina.

• This defect is because: (i) The focal length of the eye lens is too long. (ii) The eyeball has become too small.

• This defect is corrected by using a convex lens of a suitable power.

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IL Foundation Series Class 8

N (a) Near point of a hypermetropic eye

N

N’ (b) Hypermetropic eye

N

N’

(c) Correction for hypermetropic eye Fig. 6.15 Hypermetropia

6.10.3 Presbyopia The far-sightedness that occurs due to the decreasing power of accommodation with ageing is called presbyopia.

• This defect results from the weakening of ciliary muscles with age and diminishing flexibility of the eye lens.

• Presbyopia is also called old age hypermetropia.

Note: Sometimes, a person may suffer from both myopia and hypermetropia, and these defects are corrected using bi-focal lenses (a combination of concave and convex lenses).

6.10.4 Astigmatism It is a defect of vision in which a person cannot simultaneously see an object's horizontal and vertical views with the same clarity.

Cause of astigmatism: This defect occurs when the cornea of the eye is not perfectly spherical.

Thus, the eye focuses well on the objects that are in one direction but cannot focus well on the objects in the perpendicular direction.

Correction of astigmatism: Astigmatism can be corrected with cylindrical lenses. They have different curvatures in the horizontal and vertical directions, so they can be oriented suitably to compensate for the irregularities in the cornea, as shown in Figure 6.15.

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a)

Image formed on the retina

b) cylindrical lens Image formed on the retina Fig. 6.16 Astigmatism

6.10.5 Cataract and vision loss Cataract condition: In old age, the eye lens may develop cataracts, becoming milky and cloudy.

Vision impact: Cataracts can lead to partial or complete vision loss.

Solution: Vision can be restored through cataract surgery.

Example: A student finds the writing on the blackboard blurred and unclear when sitting at the last desk in the classroom. However, he is able to see well when sitting at the front desk at an approximate distance of 2 m from the blackboard. a) Name the defect of vision the student is suffering from. Also, list two causes of this defect. b) Name the kind of lens that would enable him to see well when he is seated at the last desk.

Solution: a) The vision defect is myopia. The causes of this defect are: • Elongation of the eyeball.

• Excessive curvature of the eye lens. b) A concave lens of a suitable focal length is used to correct myopia.

6.11 CARE OF THE EYES Proper eye care is crucial for maintaining good vision and overall eye health. Here are some essential practices to ensure your eyes stay healthy.

• Regular check-ups: Schedule regular check-ups with an eye specialist to monitor and address potential issues.

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IL Foundation Series Class 8

• Use of suitable spectacles: If prescribed, wear suitable spectacles to correct vision and alleviate eye strain.

• Optimal lighting conditions: Ensure proper lighting when reading or working. Insufficient light can lead to eyestrain, while excessive light, such as sunlight or powerful lamps, may cause retinal injury.

• Avoid direct sun or light exposure: Never stare directly at the sun or powerful lights, as this can harm the retina.

• Avoid eye rubbing: Refrain from rubbing your eyes, especially if dust particles enter.

Instead, wash your eyes with clean water. If issues persist, consult a doctor.

• Frequent eye washing: Wash your eyes regularly with clean water to keep them refreshed and free from irritants.

• Maintain a normal reading distance: Read at a comfortable and normal distance to prevent unnecessary strain. Avoid holding books too close or too far from your eyes.

• Ensure adequate vitamin A intake: Include vitamin A-rich foods in your diet to support eye health. Foods like raw carrots, broccoli, green vegetables (such as spinach), cod liver oil, eggs, milk, curd, cheese, butter, papaya, and mango are excellent sources of vitamin A.

6.12 VISUALLY IMPAIRED PERSONS CAN READ AND WRITE The most popular resource for visually challenged persons is Braille. Louis Braille developed a system for visually challenged persons and published it in 1821. The present system was adopted in 1932.

Braille System: The Braille system comprises 63 dot patterns or characters, with each character representing a letter, a combination of letters, a common word, or a grammatical sign. These dots are systematically arranged in cells of two vertical rows, each with three dots. People who cannot see are called 'visually challenged'. They can read and write using Braille Script using their sense of touch. To make it easier to sense the dots, they are raised slightly.

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LIGHT

A

B

C

D

E

F

G

H

I

J

K

L

M

N

O

P

Q

R

S

T

U

V

W

X

Y

Z

0

1

2

3

4

5

6

7

8

9

Fig. 6.17 Braille system

QUICK REVIEW • Light is a form of energy that causes the sensation of sight.

• Light comes back into the same medium from a boundary separating any two media, which is called reflection.

• According to the laws of reflection, the incident ray, the normal at the point of incidence, and the reflected ray all lie in the same plane, and the angle of incidence is equal to the angle of reflection.

• In any image formed by a mirror, the left of the object appears on the right, and the right of the object appears on the left. This is known as lateral inversion.

• Multiple images of an object are formed when two mirrors are inclined to each other.

• Number of images between two plane mirrors: If the position of the object is symmetrical with respect to the two mirrors, then: n= =

2π θ

-1 (if 2π/θ is even)

θ

(otherwise)

2π

• If the position of the object is symmetrical with respect to the two mirrors, then: n=

2π θ

-1.

• Splitting of light into its constituent colours is known as dispersion of light.

• The main functional parts of an eye are the cornea, iris, pupil, lens, retina, and optic nerves.

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IL Foundation Series Class 8

• The muscles attached to the eye lens can change their thickness to enable us to see near and distant objects. This feature of the eye is called accommodation.

• The impression of an image does not vanish immediately from the retina. It persists there for about 1/16th of a second.

• The most comfortable distance at which one can read with a normal eye is about 25 cm.

• Certain individuals have the ability to see nearby objects clearly but struggle with distant vision. In contrast, others face the opposite scenario, where distant objects are clear, but nearby ones appear blurry. However, these vision issues can be corrected with appropriate corrective lenses.

• Louis Braille developed the Braille system for visually challenged persons and published it in 1821.

• People who cannot see are called visually challenged. They can read and write using Braille Script.

WORKSHEET - 1 MULTIPLE CHOICE QUESTIONS WITH SINGLE CORRECT ANSWER I. Reflection of light

1. The angle of incidence is the angle between: a. The incident ray and the surface of the mirror b. The reflected ray and the surface of the mirror c. The normal to the surface and the incident ray d. The normal to the surface and the reflected ray 2. The angle between an incident ray and the normal is 30°. The angle between the incident ray and the reflected ray is: a. 30°

b. 60°

c. 90°

d. None of these

3. If a ray of light strikes a mirror surface at 60°, then the angle of incidence will be: a. 60°

b. 30°

c. 120°

d. 90°

4. What kind of images are always formed behind the mirror? a. Enlarged images

b. Small images

c. Real images

d. Virtual images

5. If you stand in front of a plane mirror and hold your left ear, your image: a. Holds its left ear

b. Holds its right ear

c. Holds both the ears

d. Does not hold any ear

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LIGHT

6. We see objects because: a. The light scattered from them falls on the eye b. The light reflected from the object reaches our eyes c. The light emitted by them falls on the eye d. All of the above 7. A virtual image is one which: a. Can be taken on a screen b. Cannot be taken on a screen c. Sometimes can be and sometimes cannot be taken on a screen d. None of these 8. The nature of the image formed by a plane mirror is: a. Laterally inverted

b. Virtual and erect

c. Of the same size as the object

d. All the above are correct

9. What happens to the size of the image in a plane mirror as the object moves closer to the mirror? a. The size increases.

b. The size decreases.

c. The size remains the same.

d. The size becomes unpredictable.

10. When the reflection takes place on a perfect smooth plane surface, then it is called: a. Diffused reflection

b. Normal reflection

c. Complete reflection

d. Regular reflection

11. A ray reflected successively from two plane mirrors inclined at a certain angle undergoes a deviation of 300°. The angle of inclination between the mirrors is: a. 15°

b. 60°

c. 30°

d. 0°

12. What is the angle of deviation for a ray which is incident at an angle of 45° on the plane mirror? a. 0°

b. 45°

c. 90°

d. 180°

13. What is the angle of deviation for a ray which is incident at an angle of 60° on the plane mirror? a. 60°

b. 45°

c. 90°

d. 180°

14. When the angle of incidence is 40°, the angle of reflection is: a. 80°

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b. 50°

c. 20°

d. 40°

IL Foundation Series Class 8

15. Assertion (A): Angle of incidence and glancing angle of incidence are complementary.

Reason (R): Normal is always perpendicular to plane mirror. a. Both A and R are true and R is the correct explanation of the A b. Both A and R are true, and R is not the correct explanation of A c. A is correct, but R is incorrect d. A is incorrect, but R is correct II. Multiple reflections of light

1. The number of images formed by two plane mirrors, if the angle between them is 60°, is: a. 5

b. 6

c. 7

d. 8

2. __________ is the application of multiple reflections of light. a. Lateral inversion

b. Plane mirror

c. Kaleidoscope

d. None

3. The number of images formed when the two plane mirrors are kept parallel to each other are: a. Infinite

b. 100

c. 4

d. 16

4. When two plane mirrors are placed at an angle of 120o to each other, how many images are formed?. a. 6

b. 4

c. 2

d. 1

5. Find out the inclination between the two mirrors if 11 images have formed: a. 30o

b. 45o

c. 60o

d. 90o

c. Six colours

d. Eight colours

c. Green

d. Blue

III. Dispersion

1. White light is composed of: a. Five colours

b. Seven colours

2. Which one of the following is not a primary colour? a. Yellow

b. Red

3. On entering a glass prism, the sun rays are: a. Deviated but not dispersed

b. Deviated and dispersed

c. Dispersed but not deviated

d. Neither deviated nor dispersed

IV. The human eye

1. Light enters the eye through: a. Pupil

b. Eye lens

c. Cornea

d. Retina

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2. The function of the lens in the human eye is: a. To form a real and enlarged image of objects on the retina b. To form a virtual image of objects on the retina c. To form a sharp, real image of objects on the retina d. None of these 3. The function of the lens in the human eye is to form a sharp image of objects: a. On the retina by changing its focal length b. On the retina by moving forward and backward c. On the retina without changing its focal length d. None of these 4. How does the image formed on the retina help us perceive the object without changing its shape, size, and colour? a. Image will be converted into electric signals with the help of rods and cones b. Optical nerves carry this information in the form of electric signals to the brain c. The brain will visualise the object clearly using these electric signals. d. All of these 5. How are we able to see objects clearly at long and short distances? a. Due to accommodation b. By changing the focal length of the lens c. By contraction and relaxation of the ciliary muscles d. All of these V. Eye defects and taking care of the eyes

1. Visually impaired people can read and write using: a. Electronic write

b. Digital pens

c. Braille system

d. Hearing aids

2. _______ are used to correct myopia.

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a. Plane mirrors

b. Concave lenses

c. Kaleidoscope

d. Convex lenses

IL Foundation Series Class 8

3. The defect in which the eye can see distant objects clearly but can not see nearby objects distinctly is: a. Myopia

b. Hypermetropia

c. Astigmatism

d. Cataract

WORKSHEET - 2 MULTIPLE CHOICE QUESTIONS WITH SINGLE CORRECT ANSWER 1. The objects which emit light of their own are called: a. Transparent objects

b. Translucent objects

c. Luminous object

d. Non-luminous objects

2. Light is a form of: a. Energy

b. Work

c. Power

d. Force

3. Which of the following represents the correct order of the colours in the spectrum of white light, starting from the shortest wavelength to the longest? a. Violet, Indigo, Blue, Green, Yellow, Orange, Red b. Red, Orange, Yellow, Green, Blue, Indigo, Violet c. Red, Yellow, Green, Blue, Indigo, Violet, Orange d. Violet, Blue, Green, Yellow, Orange, Red, Indigo 4. Light travels in a: a. Straight line

b. Curved line

c. Neither straight nor curved

d. None of these

5. In a plane mirror, the distance of an image is the: a. Same as that of the object

b. Greater as that of the object

c. Less as that of the object

d. More than 10 m

6. The mirror used in a kaleidoscope is a: a. Concave mirror

b. Convex mirror

c. Plane mirror

d. Convex lens

7. A lens with thick outer ends is a: a. Convex lens

b. Concave lens

c. Both a and b

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8. Glass is a: a. Transparent media

b. Opaque

c. Luminous

d. All of these

9. The lens that is used as a magnifying glass is a: a. Concave lens

b. Convex lens

c. Concave-convex lens

d. Convex-concave lens

10. Which one of the following shows lateral inversion: a. Plane mirror

b. Convex mirror

c. Concave mirror

d. All of these

11. The image formed by a plane mirror is always: a. Virtual and erect

b. Real and erect

c. Virtual and inverted

d. Real and inverted

12. The power of a lens is measured in: a. cm

b. km

c. diopter

d. m

13. The splitting of white light into its seven constituent colours is called: a. Refraction

b. Dispersion

c. Deviation

d. Reflection

14. The laws of reflection of light are valid for: a. Plane mirror

b. Concave mirror

c. Convex mirror

d. All of these

15. The focal length of the plane mirror is: a. 1

b. 1/2

c. ∞

d. 0

16. The magnification of an object due to a plane mirror is: a. +1 c. 0

b. -1 d. ∞

17. A beam of light incident on a plane mirror forms a real image on reflection. The incident beam is:

a. Parallel

b. Convergent

c. Divergent

d. Perpendicular

18. Which of the following is correct for a plane mirror? a. Object distance = Image distance c. Object size ≠ Image size

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b. The image formed is small. d. All of these

IL Foundation Series Class 8

19. A clock fixed on a wall shows the time 04:25:37. What time will its image in a plane mirror hanging on the opposite vertical wall show? a. 07:43:32

b. 07:30:32

c. 07:35:22

d. 07:53:36

20. Which of the following is the requirement for nocturnal animals like owls and bats? a. Large cornea

b. Large pupil

c. Retina with a large number of rods

d. All of the above

21. How is a rainbow formed? a. When raindrops absorb sunlight

b. When raindrops reflect sunlight

c. When raindrops disperse sunlight

d. When raindrops diffract sunlight

22. Which of the following letters will be seen without any change in a plane mirror? a. S

b. T

c. L

d. P

23. Which of the following is the characteristic of an ideal mirror? a. It absorbs all the light incident on it. b. It refracts all the light. c. It reflects all the light. d. All of the above.

24. A series of fast-moving still pictures can create an illusion of movement. Why? a. The eye can focus on very rapidly changing pictures. b. The eye is quicker than the brain. c. The eye can separate two images only when the interval of separation between them is one-sixteenth of a second. d. The optical cortex can see through rapidly moving images.

25. For a normal eye, what is the least distance of distinct vision? a. 5 cm

b. 100 cm

c. 25 cm

d. 50 cm

26. Identify the part of the human eye on which different images are formed. a. Iris

b. Pupil

c. Cornea

d. Retina

27. Identify the nature of the image formed by the eye lens of a human eye: a. Real, upright, and enlarged

b. Real, upright, and diminished

c. Real, inverted, and diminished

d. Virtual, inverted, and diminished

28. Which of the following occurs in persons suffering from myopia? a. The eyeball is shortened

b. Ciliary muscles contract

c. The eyeball elongates

d. The retina expands

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29. The number of images formed by the combination of two plane mirrors, when:

i) θ = 30°, ii) θ = 45°, iii) θ = 60°, iv) θ = 90° in assymmetrical arrangement are a. 5, 11, 7, 3

b. 3, 5, 7, 11

c. 11, 7, 5, 3

d. 11, 3, 5, 7

30. Assertion (A): When a ray of light is incident normally (perpendicularly) on the surface of a plane mirror, it reflects back along the same path.

Reason (R): The incident ray and the reflected ray make equal angles with the normal, as per the laws of reflection. a. Both A and R are true, and R is the correct explanation of A. b. Both A and R are true, but R is not the correct explanation of A. c. A is true, but R is false. d. A is false, but R is true.

31. At an instant, the hands of a watch show time 3:25. When seen through a mirror, the time that appeared will be a. 8:35

b. 9:35

c. 7:35

d. 8:25

32. Certain glasses form clear images, but not some glasses because a. The reflection from rough or irregular surfaces is diffused reflection, due to which the images formed by certain glasses are not clear. b. The reflection from a smooth surface of a mirror is called regular reflection, due to which clear images are formed by certain glasses. c. The reflection from a rough or irregular surface is called diffused reflection, due to which clear images are formed by certain glasses. d. Both a and b.

140

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ϰ͘ Ă

ϱ͘ Đ

tŽƌŬƐŚĞĞƚ Ϯ ϭ͘ ď Ϯ͘ Ă ϯ͘ Ě ϰ͘ ď ϱ͘ Đ ϲ͘ ď ϳ͘ Ă ϴ͘ ď ϵ͘ Ă ϭϬ͘ Ă ϭϭ͘ Ě ϭϮ͘ ď ϭϯ͘ Đ ϭϰ͘ Ě ϭϱ͘ Ă ϭϲ͘ Ă ϭϳ͘Ě ϭϴ͘ Ě ϭϵ͘ Ě ϮϬ͘ Ă Ϯϭ͘ Ă ϮϮ͘ Ě Ϯϯ͘ Ě Ϯϰ͘ Đ Ϯϱ͘ Ě Ϯϲ͘ Ě Ϯϳ͘ Ě Ϯϴ͘ Ě Ϯϵ͘ Ă ϯϬ͘ Đ ϯϭ͘ Ă ϯϮ͘ Ě ϯϯ͘ Ě ϯϰ͘ Đ ϯϱ͘ ď ϯϲ͘ Ě ϯϳ͘ Ě ϯϴ͘ Ă ϯϵ͘ Ă ϰϬ͘a ϰϭ͘ Ě ϰϮ͘ c ϰϯ͘ ď ϰϰ͘ b ϰϱ͘ Đ ϰϲ͘ Đ ϰϳ͘Ě ϰϴ͘ Ě ϰϵ͘ Ă ϱϬ͘ Đ ϱϭ͘ Ě ϱϮ͘ Đ ϱϯ͘ ď ϱϰ͘ Ă ϱϱ͘ Đ ϱϲ͘ Đ ϱϳ͘ Ě ϱϴ͘ Ě ϱϵ͘ Ă ϲϬ͘ Ă ϲϭ͘ ď ϲϮ͘ Đ ϲϯ͘ Ă ϲϰ͘ Ă ϲϱ͘ Ě ϲϲ͘ Ă ϲϳ͘ Đ ϲϴ͘ Ě ϲϵ͘ Ě

Ϯ͗ &Z/ d/KE tŽƌŬƐŚĞĞƚ ϭ /͘ &ŽƌĐĞ ŽĨ ĨƌŝĐƚŝŽŶ ĂŶĚ ĨĂĐƚŽƌƐ ĂĨĨĞĐƚŝŶŐ ĨƌŝĐƚŝŽŶ ϭ͘ ď Ϯ͘ ď ϯ͘ Ě ϰ͘ Đ ϱ͘ Ă ϲ͘ Ă ϳ͘ ď ϴ͘ Ě ϵ͘ Ě ϭϬ͘ ď ϭϭ͘ď ϭϮ͘Ă //͘ &ƌŝĐƚŝŽŶ͗ ŶĞĐĞƐƐĂƌLJ Ğǀŝů ϭ͘ Ě Ϯ͘ Ă ///͘ dLJƉĞƐ ŽĨ ĨƌŝĐƚŝŽŶ ϭ͘Ă Ϯ͘ a ϯ͘ Ě ϰ͘ Đ ϱ͘ Ě ϲ͘ Ă ϳ͘ Ă ϴ͘ Ă ϵ͘ a ϭϬ͘ Đ ϭϭ͘ď ϭϮ͘Ă ϭϯ͘Ă /s͘ /ŶĐƌĞĂƐŝŶŐ ĂŶĚ ƌĞĚƵĐŝŶŐ ĨƌŝĐƚŝŽŶ ĂŶĚ ĨůƵŝĚ ĨƌŝĐƚŝŽŶ ϭ͘ Ă Ϯ͘ Đ ϯ͘ Ă tŽƌŬƐŚĞĞƚ Ϯ ϭ͘ Đ Ϯ͘ Ă ϯ͘ Ă ϰ͘ Ă ϱ͘ Ě ϲ͘ Đ ϳ͘ Đ ϴ͘ Ě ϵ͘ Đ ϭϬ͘ Đ ϭϭ͘Ă ϭϮ͘ Ě ϭϯ͘ ď ϭϰ͘ Đ ϭϱ͘ Đ ϭϲ͘ Ě ϭϳ͘ Ě ϭϴ͘ Ě ϭϵ͘ Đ ϮϬ͘ Đ Ϯϭ͘ Ě ϮϮ͘ Đ Ϯϯ͘ Ě Ϯϰ͘ Ă Ϯϱ͘ Ě Ϯϲ͘ Ă Ϯϳ͘ Ě Ϯϴ͘ c Ϯϵ͘Ě ϯϬ͘ Ě ϯϭ͘ Ě ϯϮ͘ Ě ϯϯ͘ Ă ϯϰ͘ Ě ϯ͗ ^KhE tŽƌŬƐŚĞĞƚ ϭ /͘ /ŶƚƌŽĚƵĐƚŝŽŶ ƚŽ ƐŽƵŶĚ ĂŶĚ ƉƌŽĚƵĐƚŝŽŶ ŽĨ ƐŽƵŶĚ ϭ͘ ď Ϯ͘ Ă ϯ͘ Ă ϰ͘ Đ ϱ͘ Ě ϲ͘ Ă ϳ͘ ď ϴ͘ Ă //͘ ^ŽƵŶĚ ǁĂǀĞƐ ĂŶĚ ůŝŐŚƚ ǁĂǀĞƐ͕ ƉƌŽƉĂŐĂƚŝŽŶ ŽĨ ƐŽƵŶĚ ĂŶĚ ƐƉĞĞĚ ŽĨ ƐŽƵŶĚ ϭ͘ Đ Ϯ͘ Ă ϯ͘ Ě ϰ͘ Ă ϱ͘ ď ϲ͘ Đ ϳ͘ Ă ϴ͘ Ă ///͘ dŚĞ ŚƵŵĂŶ ĞĂƌ ĂŶĚ ĐŚĂƌĂĐƚĞƌŝƐƚŝĐƐ ŽĨ Ă ƐŽƵŶĚ ǁĂǀĞ

141

E^t Z < z ϭ͘ Ă Ϯ͘ ď ϯ͘ Đ ϰ͘ Đ ϱ͘ Ă ϲ͘ Đ ϳ͘ ď ϴ͘ Đ ϵ͘ Ă ϭϬ͘ Ă ϭϭ͘ Ă /s͘ ƵĚŝďůĞ ĂŶĚ ŝŶĂƵĚŝďůĞ ƐŽƵŶĚƐ͕ ƌĞĨůĞĐƚŝŽŶ ŽĨ ƐŽƵŶĚ͕ ĂŶĚ ŶŽŝƐĞ ĂŶĚ ŵƵƐŝĐ ϭ͘ ď Ϯ͘ ď ϯ͘ ď ϰ͘ Ă ϱ͘ Ă ϲ͘ Đ ϳ͘ Ă ϴ͘ Đ ϵ͘ Ă tŽƌŬƐŚĞĞƚ Ϯ ϭ͘ ď Ϯ͘ Ě ϯ͘ Đ ϲ͘ Đ ϳ͘ ď ϴ͘ Đ ϭϭ͘ Đ ϭϮ͘ Ě ϭϯ͘ Ă ϭϲ͘ ď ϭϳ͘ Ě ϭϴ͘ Ě Ϯϭ͘ Ě ϮϮ͘ ď Ϯϯ͘ Ă Ϯϲ͘ Ă Ϯϳ͘ Ă Ϯϴ͘ Ě ϯϭ͘ Ě ϯϮ͘ Ě ϯϯ͘ Ě ϯϲ͘ Ě ϯϳ͘ Ě ϯϴ͘ ď ϰϭ͘ Ě ϰϮ͘ Đ ϰϯ͘ Ě ϰϲ͘ Đ ϰϳ͘ Ă ϰϴ͘ Ă

ϰ͘ Ă ϵ͘ Ă ϭϰ͘ Đ ϭϵ͘ Ă Ϯϰ͘ Ě Ϯϵ͘ Ě ϯϰ͘ Ě ϯϵ͘ Ă ϰϰ͘ Ě ϰϵ͘ Ă

ϱ͘ ď ϭϬ͘ Đ ϭϱ͘ ď ϮϬ͘ Ě Ϯϱ͘ Đ ϯϬ͘ Ě ϯϱ͘ ď ϰϬ͘ Ě ϰϱ͘ Đ

142

ϯ͘ Ě ϴ͘ Đ

ϰ͘ Ě ϵ͘ Đ

ϭϮ͘ Ă ϭϳ͘ Ă ϮϮ͘ Ă Ϯϳ͘ Ă

ϱ͘ Ă ϭϬ͘ Ă

ϭϯ͘ ď ϭϴ͘ Ě Ϯϯ͘ Ă Ϯϴ͘ ď

ϭϰ͘ ď ϭϵ͘ Ă Ϯϰ͘ Ă Ϯϵ͘ Ă

ϭϱ͘ Ě ϮϬ͘ ď Ϯϱ͘ Đ ϯϬ͘ Ă

ϱ͗ ^KD E dhZ > W, EKD E tŽƌŬƐŚĞĞƚ ϭ /͘ ,ŝƐƚŽƌLJ ŽĨ ůŝŐŚƚŶŝŶŐ ĂŶĚ ŵĞƚŚŽĚƐ ŽĨ ĐŚĂƌŐŝŶŐ ϭ͘ Đ Ϯ͘ Đ ϯ͘ Ă ϰ͘ď ϱ͘ ď //͘ dLJƉĞƐ ŽĨ ĐŚĂƌŐĞƐ ĂŶĚ ƚƌĂŶƐĨĞƌ ŽĨ ĐŚĂƌŐĞ ϭ͘ Ě Ϯ͘ Ă ϯ͘ Ě ϰ͘ ď ϱ͘ ϲ͘ ď ϳ͘ ď ϴ͘ ď ϵ͘ Ă ϭϬ͘Ě ///͘ ^ĂĨĞƚLJ ƉƌĞĐĂƵƚŝŽŶƐ ĚƵƌŝŶŐ ůŝŐŚƚŶŝŶŐ ĂŶĚ ƚŚƵŶĚĞƌƐƚŽƌŵƐ ϭ͘ Đ Ϯ͘ Đ ϯ͘ Ě ϰ͘ Đ ϱ͘ Ě ϲ͘ Đ ϳ͘ ď /s͘ ĂƌƚŚƋƵĂŬĞƐ ϭ͘ Ă Ϯ͘ Đ ϯ͘ ď tŽƌŬƐŚĞĞƚ Ϯ ϭ͘ Ě Ϯ͘ Ě ϯ͘ Ă ϲ͘ ď ϳ͘ Đ ϴ͘ď ϭϭ͘Đ ϭϮ͘ Đ ϭϯ͘ Ě ϭϲ͘ Đ ϭϳ͘ Đ ϭϴ͘ ď Ϯϭ͘ Ă ϮϮ͘ ď Ϯϯ͘ ď

ϰ͗ , D/ > && d^ K& > dZ/ hZZ Ed tŽƌŬƐŚĞĞƚ ϭ /͘ ŽŶĚƵĐƚŽƌƐ ĂŶĚ ŝŶƐƵůĂƚŽƌƐ ϭ͘ ď Ϯ͘ Ă ϯ͘ ď ϰ͘ Ă ϱ͘ Ě ϲ͘ ď ϳ͘ Ă ϴ͘ Ă ϵ͘ Ă ϭϬ͘ Ă //͘ Ž ůŝƋƵŝĚƐ ĐŽŶĚƵĐƚ ĞůĞĐƚƌŝĐŝƚLJ͍ ϭ͘ Đ Ϯ͘ Ă ϯ͘ Ě ϰ͘ Ě ϱ͘ ď ϲ͘ Ě ϳ͘ Ě ϴ͘ ď ϵ͘ Đ ϭϬ͘ ď ///͘ ŚĞŵŝĐĂů ĞĨĨĞĐƚƐ ŽĨ ĞůĞĐƚƌŝĐ ĐƵƌƌĞŶƚ ϭ͘ ď Ϯ͘ ď ϯ͘ Ă ϰ͘ Ă ϱ͘ ď ϲ͘ Ě ϳ͘ Ě ϴ͘ Ě ϵ͘ ď ϭϬ͘ Ă /s͘ ůĞĐƚƌŽƉůĂƚŝŶŐ ϭ͘ Ă Ϯ͘ ď ϯ͘ Ă ϰ͘ Đ ϱ͘ Ă ϲ͘ Ě ϳ͘ Ě ϴ͘ ď ϵ͘ ď ϭϬ͘ Ă tŽƌŬƐŚĞĞƚ Ϯ ϭ͘ Ě Ϯ͘ Ă ϲ͘ ď ϳ͘ Ě

ϭϭ͘ ď ϭϲ͘ Ě Ϯϭ͘ Ě Ϯϲ͘ Ě

ϰ͘ Ě ϵ͘ Đ ϭϰ͘ Ă ϭϵ͘ Ă Ϯϰ͘ Ě

ϱ͘ ď ϭϬ͘ Ě ϭϱ͘ Ě ϮϬ͘ ď Ϯϱ͘ Ě

ϲ͗ >/',d tŽƌŬƐŚĞĞƚ ϭ /͘ ZĞĨůĞĐƚŝŽŶ ŽĨ ůŝŐŚƚ ϭ͘ Đ Ϯ͘ ď ϯ͘ ď ϰ͘ Ě ϱ͘ b ϲ͘ ď ϳ͘ ď ϴ͘ Ě ϵ͘ Đ ϭϬ͘ Ě ϭϭ͘ Đ ϭϮ͘ Đ ϭϯ͘ Ă ϭϰ͘ Ě ϭϱ͘ Ă //͘ DƵůƚŝƉůĞ ƌĞĨůĞĐƚŝŽŶƐ ŽĨ ůŝŐŚƚ ϭ͘ Ă Ϯ͘ Đ ϯ͘ Ă ϰ͘ Đ ϱ͘ Ă ///͘ ŝƐƉĞƌƐŝŽŶ ϭ͘ ď Ϯ͘ Đ ϯ͘ ď /s͘ dŚĞ ŚƵŵĂŶ ĞLJĞ ϭ͘ Đ Ϯ͘ c ϯ͘ Ă ϰ͘ Ě ϱ͘ Ě

E^t Z < z s͘ LJĞ ĚĞĨĞĐƚƐ ĂŶĚ ƚĂŬŝŶŐ ĐĂƌĞ ŽĨ ƚŚĞ ĞLJĞƐ ϭ͘ Đ Ϯ͘ ď ϯ͘ ď tŽƌŬƐŚĞĞƚ Ϯ ϭ͘ Đ Ϯ͘ Ă ϯ͘ a ϲ͘ Đ ϳ͘ ď ϴ͘ Ă ϭϭ͘Ă ϭϮ͘ Đ ϭϯ͘ď ϭϲ͘ Ă ϭϳ͘ď ϭϴ͘ Ă Ϯϭ͘ Đ ϮϮ͘ ď Ϯϯ͘ Đ Ϯϲ͘ Ě Ϯϳ͘ Đ Ϯϴ͘Đ ϯϭ͘ Ă ϯϮ͘Ě

ϰ͘ Ă ϵ͘ ď ϭϰ͘ Ě ϭϵ͘ Đ Ϯϰ͘ Đ Ϯϵ͘ Đ

ϱ͘ Ă ϭϬ͘ Ě ϭϱ͘ Đ ϮϬ͘ Ě Ϯϱ͘ Đ ϯϬ͘ Ă

143