PHYSICS MEASUREMENT OF LENGTH, VOLUME, TIME AND MASS

Measurement of Length, Volume, Time and Mass Least Count of a Measuring Instrument   

The least count of an instrument is the smallest measurement that can be taken accurately with it. The least count of an instrument is the value of the smallest division on its scale. Smaller the least count of an instrument, the measurement done by using it is even more accurate.

Measurement of Length with a Metre Scale    

A metre scale is a scale with length one metre which is graduated in cm and has subdivisions in mm. There are 10 subdivisions in each cm. The value of one small division on metre scale is 1 mm. Thus, its least count is 1 mm. Precautions should be taken while measuring the length of an object: Limitation of a metre scale is that, it can measure length correctly up to one decimal place of a centimetre.

Principle of Vernier   

Two scales are used in this technique. One is the main scale and the other is called vernier scale. The least count of vernier is equal to the difference between the values of one main scale division and one vernier scale division. This is called vernier constant. ‘n’ divisions of vernier is equal to n-1 divisions of main scale. Therefore, value of one division of vernier is 

n  1 x .

L.C. 

n

Value of 1 main scale division  x 

Total number of divisions on vernier n 

Vernier Callipers 

A vernier calliper is also called slide calliper.

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PHYSICS MEASUREMENT OF LENGTH, VOLUME, TIME AND MASS 

The main parts of vernier callipers and their functions are given below. Part

Main scale Vernier scale

Function To measure the internal diameter of a hollow cylinder or pipe. To measure length of a rod, diameter of a sphere, external diameter of a hollow cylinder. To measure length correct up to 1 mm. To measure length correct up to 0.1 mm.

Strip

To measure depth of a beaker or a bottle.

Inside jaws Outside jaws

Least count of a vernier calliper is given as Value of 1 main scale division  x  L.C.  Total number of divisions on vernier n 

Zero error in vernier callipers: The zero error is equal to the distance between the zero of the main scale and the zero of the vernier scale.

 

Kinds of zero error: There are two kinds of zero error possible- Positive and negative zero error.  Positive zero error: If the zero mark of the vernier scale is on the right of the zero mark of the main scale, the zero error is said to be positive.  Negative zero error: If the zero mark of the vernier scale is on the left of the zero mark of the main scale, the zero error is said to be negative. The correction due to zero error, that is, correct measure of the length is;

Positive zero error gets subtracted and negative zero error gets added to the observed reading.

Principle of Screw    

The pitch of the screw is the distance moved by the screw along its axis in one complete rotation of its head. There are graduations along the circumference of the head of the screw. There are about 50 to 100 graduations. This is called circular scale or head scale. The pitch of the screw is 1 mm and if there are 100 divisions on the circular scale, then the least count of screw is 1/100 = 0.01 mm = 0.001 cm. The least count of a screw is the distance moved by it in rotating the circular scale by one division. Pitch of screw L.C.  Total number of divisions on circular scale

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PHYSICS MEASUREMENT OF LENGTH, VOLUME, TIME AND MASS

Screw Gauge

The main parts of screw gauge and their functions are given below. Part Circular scale Main scale Sleeve Thimble Ratchet

Function Helps to read length correct up to 0.01 mm. To read length correct up to 1 mm. To mark main scale and base line. To mark circular scale. To advance the screw by turning it till the object is gently held between the stud and spindle of screw.

Pitch And Least Count: The pitch of a screw gauge is the linear distance moved by its screw on the main scale when circular scale completes one full rotation. The least count is the linear distance moved by its screw on the main scale when the circular scale is rotated by one division. L.C. 

Pitch of screw Total number of divisions on circular scale

 

Kinds of zero error: There are two kinds of zero error possible- Positive and negative zero error.  Positive zero error: If the zero mark of the circular scale is below the base line of the main scale, the zero error is said to be positive.  Negative zero error: If the zero mark of the circular scale is above the base line of the main scale, the zero error is said to be negative.

The correction due to zero error, that is, correct measure of the length is; Correct reading  Observed reading  Zero error

Backlash error: Due to wear and tear of the threads of the screw, it is observed that on reversing the direction of rotation of the thimble, the tip of the screw does not start moving in opposite direction at once, but it remains stationary for some part of rotation. The error caused due to this effect is called backlash error.

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PHYSICS MEASUREMENT OF LENGTH, VOLUME, TIME AND MASS

Volume     

The space occupied by a body is called its volume. The SI unit of volume is cubic metre, that is, metre3 = m3. Volume of liquids is expressed in litre. The relation between litre and m 3 is 1000 litre  1 m3 . Other relations are: 1 m3  100 cm   106 cm3 3

1 litre  103 m3  103 cm3 1 ml  1 cm3  106 m3

Measurement of Volume 

Volume of a regular shaped object:  In order to find the volume of an object, its dimensions are to be measured.  The dimensions can be measured by metre scale, vernier callipers or screw gauge.

Instruments for measuring volume of a liquid or an irregular shaped object: a. Burette: o A burette is a narrow glass tube provided with a tap at the bottom end.

o The area of cross-section of the tube is 1 cm2. o The tube is graduated in ml with each ml divided into 10 parts.

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PHYSICS MEASUREMENT OF LENGTH, VOLUME, TIME AND MASS b. Pipette: o A pipette is a glass tube with a cylindrical bulb in the middle. o The tube is drawn in such a way that, a narrow nozzle is formed at its lower end.

o A graduation mark is etched on its stem near the upper end. When the pipette is filled with the liquid up to this level, it is said to contain a fixed volume of liquid. This fixed value is written on the bulb of the pipette. c. Measuring flask: o A measuring flask has a long narrow neck provided with a stopper.

o A graduation mark is etched on the neck. When the flask is filled with the liquid up to this level, it is said to contain a fixed volume of liquid. This fixed value is written on the flask. d. Measuring cylinder: o A measuring cylinder is a glass cylinder graduated in ml.

o It is used to measure or pour a desired volume of a liquid. The volume will be equal to the capacity marked on it.

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PHYSICS MEASUREMENT OF LENGTH, VOLUME, TIME AND MASS 

Measuring volume of an irregular solid by displacement method: CASE I: When solid is heavier than water.  When the solid is lowered gently in it and immersed completely, the level of water rises. This reading is also to be noted.

 

The difference in the two readings gives the volume of solid. If the difference is 10 ml, then the volume of solid is 10 cm 3.

CASE II: When solid is lighter than water.

   

When the sinker is lowered gently in it and immersed completely, the level of water rises. This reading is also to be noted. Now, tie the sinker and lighter solid together and lower them into water. Note the reading of lower meniscus again. The difference in the two readings, that is, with sinker and with sinker and solid gives the volume of the solid. Thus, if the difference is 5 ml, then the volume of solid is 5 cm 3.

CASE III: When solid is soluble in water.  For this purpose, water is replaced with a liquid like spirit, kerosene, etc.  These liquids should be lighter than the solid and also the solid should not dissolve in them.

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PHYSICS MEASUREMENT OF LENGTH, VOLUME, TIME AND MASS

Measurement of Time Stop Watch o A stop watch consists of a circular dial graduated in 60 equal spaced divisions. Each division is equal to 1 second. o A small dial is also provided inside the big dial. This dial enables us to record time in minutes.

o A knob is provided at the top of the frame of watch for winding purposes. o The knob is pressed at the start of event and pressed again to stop time at the end of event.

Stop Clock o It is a table clock and is bigger than a stop watch. o It has a circular dial graduated in 60 equal spaced divisions. Each division is equal to 1 second. o The minuteâ&#x20AC;&#x2122;s hand is set to zero by a knob provided at the back of clock.

o The clock is also provided with an index hand. It is usually painted red. o A horizontal rod is provided at the back of the frame to start or stop the clock. When the rod is pushed to right, it starts the clock. When it is pushed to left, it stops the clock.

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PHYSICS MEASUREMENT OF LENGTH, VOLUME, TIME AND MASS

Simple Pendulum: 

A simple pendulum is a heavy point mass called the bob suspended from a rigid support by a massless and inextensible string.

When the bob at rest position is moved to one side and released, the pendulum is set in motion. The rest position is called the mean position of the pendulum. 

Terms related to simple pendulum: o Oscillation: One complete to and from motion of the bob of the pendulum is called one oscillation. o Period of oscillation or time period: It is the time taken to complete one oscillation. It is denoted by T. Its unit is second (s). o Frequency of oscillation: It is the number of oscillations made in one second. It is denoted by f or n. Its unit is per second (s-1) or hertz (Hz). 1 o frequency f  T o Amplitude: The maximum displacement of the bob from its mean position on either side is called amplitude of oscillation. It is denoted by a or A. Its unit is metre (m). o Effective length of the pendulum: It is the distance of the mean point of oscillation to the point of suspension. It is denoted as l.

Measurement of time period of a simple pendulum: o The time period is directly proportional to square root of length. T l T2  l l  constant T2

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PHYSICS MEASUREMENT OF LENGTH, VOLUME, TIME AND MASS 

Graph of variation of time period T with length l: o A graph of T v/s l is plotted which is a straight line as shown below.

Graph of T2 v/s l: o The graph of T2 v/s l is a straight line indicating that T2 is directly proportional to l for a pendulum.

o The slope from the graph is given as; Slope 

PR T12  T22 42   QR l1  l2 g

Factors affecting time period: o The time period of oscillation of a pendulum is directly proportional to the square root of its effective length. T l

o The time period of oscillation of a pendulum is inversely proportional to the square root of acceleration due to gravity. 1 T g o The time period of oscillation of a pendulum does not depend on the mass or material of the body suspended. o The time period of oscillation of a pendulum does not depend on the extent of swing, that is, amplitude on either side. o Thus, the time period of pendulum is: T  2

l g

Seconds pendulum: o The pendulum in clocks at our homes is a seconds pendulum. This pendulum has a time period of 2 s.

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PHYSICS MEASUREMENT OF LENGTH, VOLUME, TIME AND MASS

Measurement of Mass: A Beam Balance for Comparison of Masses   

The amount of matter contained in a body is its mass. It is measured by a beam balance by comparing it with a known standard mass. A beam balance works on the principle of moments. According to this, “in equilibrium, the moment due to the weight of an object on one side of beam is equal to the moment due to the standard weights on the other side of the beam”. One moment is clockwise and the other is anticlockwise.

Precautions in using a beam balance:  The lever should be turned gently, in order to prevent the knife edges from chipping.  The beam should be lowered before adding or removing weights from the pan.  Wet and hot objects should not be placed on the pan.  The weights should be replaced into the weight box after weighing.  The weights should be carried with forceps.  When near the actual weight, the weights should always be tried in ascending order.

Conditions for a true balance: A balance to be true, must satisfy the following two conditions:  Both the arms must be of equal lengths, and  Both the arms must be of equal weights.

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ICSE Class IX Physics Measurement of Length Volume Time and Mass - TopperLearning

The least count of an instrument is the smallest measurement that can be taken accurately with it.

ICSE Class IX Physics Measurement of Length Volume Time and Mass - TopperLearning

The least count of an instrument is the smallest measurement that can be taken accurately with it.