Important Question for class 12 Physics Academic team of entrancei prepared selected questions for class 12 Physics download your free copy of class 12 Physics questions from entrancei . do find NCERT solutions for class 12 Physics Prob 1.
!
D ( d)
If the mid-points of the consecutive sides of any quadrilateral arc connected by straight line segments, prove that the resulting quadrilateral is a parallelogram.
Prob 2. Sol:
D (c ) Q
S !
() ! ! ! ! ! a) ( Let a , b , c and d are the position vector of A, B, C and D. Hence position vector of mid points P, Q, R and S will be ! ! ! ! ! ! ! ! a+b b+c c +d d+a , , and , respectively. 2 2 2 2 ! ! ! ! ! ! !!!" b+c a+c c -a We have, PQ = position vector Q - positive vector of P = = 2 2 2 ! ! """! c! + d d + a! c! - a! and SR = = 2 2 2 !!!" !!!" Hence, PQ = SR Similarly, we can show that, !!!" !!!" QR = PS \ PQRS is a parallelogram. A
Sol:
!
R
P
! Find the angle that the vector A = 2iˆ + 3ˆj - kˆ makes with y-axis y Ay 3 3 Here, cos q = = = 2 2 2 A 14 ( 2 ) + ( 3 ) + ( -1) A y
\
B b
! A = 2iˆ + 3jˆ - kˆ
q
æ 3 ö q = cos-1 ç ÷ è 14 ø
x z
Prob 3.
(
force. Sol:
)
(
)
A force 3iˆ + 4ˆj N acts on a body and displace it by 3iˆ + 4ˆj m. Find the work done by the
! ! Force, F = 3iˆ + 4ˆj N and displacement S = 3iˆ + 4ˆj m
(
)
We know that,
(
)
!! Work done by the force W = F.S = 3iˆ + 4ˆj . 3iˆ + 4ˆj = (3.3).1 + (4.4).1 = 9 + 16 = 25 Joule
(
)(
)
Note: work is a scalar quantity. Prob 4.
A man wants to reach point B on the opposite bank of a river flowing at a speed as shown in the figure. What minimum speed relative to water should the man have so that he can reach point B? In which direction should he swim?
B 30°
A
Entrancei
u
Sol:
Resultant of v and u should be along AB. Component ! of v s (absolute velocity of swimmer) along x and y direction are vx = u - v sin q and vy = v cos q vy 1 v cos q = \ tan 30° = or, vx 3 u - v sin q or,
v=
u
=
B v
y
q 30°
x A
u , [! sin (A +B) = sin A cos B + cos A + sin B] 2sin ( q + 60° )
sin q + 3 cos q q + 60° = 90° Þ q = 30° and, vmin = u/2
Prob 5.
Sol:
A man crosses a river in a boat. If he cross the river in minimum time be taken 10 minutes with a drift 120 m. If he crosses the river taking shortest path, he takes 12.5 minutes, find (a) width of the river (b) velocity of the boat w.r.t. water (c) speed of the current. Let vr = velocity of river Vmr = velocity of man in still water d = width of river Given, tmin = 10 minutes d or, = 10 v mr Drift in this case will be x = vrt \ 120 = 10 vr Shortest path is taken when vm is along AB In this case vm =
d d = 2 v m v mr - v r2 Solving these three equations, we get, vmr = 20 m/min vm = 12 m/min and d = 200 m
Sol:
vm
vmr . . . (1)
d
A
. . . (2)
2 v mr - v r2
Now, 12.5 =
Prob 6.
vr B
. . . (3)
Rain, pouring down at an angle a with the vertical has a speed of 10 m/s. A girl runs against the rain with a speed of 8 m/s and sees that the rain makes an angle b with the vertical, then establish the reaction between a and b. ! ! ! ! We know that v r = v gr + v g vg ! ! ! x or, v gr = v r - v g a b ! ! ! When, a girl start running, then component of v gr in x and vr v gr y-directions are vx = (vg + vr sin a) = 8 + 10 sin a and vy = -vr cos a = -10 cos a -v x 8 + 10 sin a Here, tan b = = vy 10cos a
y
vx v gr
Entrancei
b
vy
Prob 7.
Two trains, each of 50 m length are moving parallel on parallel tracks towards each other with speeds of 10 m/s and 15 m/s. find the time, when they pass each other.
Sol:
Length of a train = " = 50 m; speed of train 1 = v1 = 10 m/s and speed of train 2 = v2 = 15 m/s. If they cross each other, then relative velocity of 1 w.r.t. 2 = v1 + v2 = (10 + 15) m/s = 25 m/s Total distance covered 50 + 50 = 4 sec Hence, time taken = = Relative velocity of 1 w.r.t. 2 25
Entrancei