Laws of motion: Numerical

Que.1: A bus weighing 900kg is at rest on a bus stand. What is its linear momentum?
Que.2: Show that:
(1) Coefficient of friction is equal to the tangent of the angle of friction.
(2) Angle repose is equal to the angle of friction.
(3) That the minimum velocity of projection at the lowest point for looping the loop is
√5gr and the minimum velocity at the top is √gr.
Que.3: A bullet of mass 0.04kg moving with a speed of 90 m/s enters a heavy wooden block
and is stopped after a distance of 60cm. what is the average resistive force exerted by the
block on the bullet?
Que.4: A 70kg man stands in contact against the wall of a cylindrical drum of radius 3m
rotating about its vertical axis with 200 revolution / minute.
Que.5: How much work a man will do in carrying a 10kg load over his head horizontally on
a smooth surface for 10meters?
Que.6: A bus starts from rest accelerating uniformaly with 4m/s2. At t= 10s, a stone dropped
out of a window of the bus 2 m high. What are the (i) magnitude of velocity and
(ii) acceleration of the stone at 10.2 s? take g= 10m/s2.
Que.7: A force acts for 10 s on a body of mass 10 kg after which the force ceases and the
body describe 50m in the nest 5 s. find the magnitude of the force.
Que.8: A truck starts from rest and rolls down a hill with constant acceleration. It travels a
distance of 400 m in 20 s. calculate the acceleration and the force acting on it if its mass is
7 metric tons.
Que.9: A force of 5N gives a mass m1 an acceleration of 8 m/s2 and a mass m2 an acceleration
of 24 m/s2. What acceleration would it give if both the masses are tied together?
Que.10: A stone of mass 5kg falls from the top of a cliff 50m high and buries 1m in sand.
Find the average resistance offered by the sand and the time it takes to penetrate.
Que.11: A bullet of mass 100g moving with a speed of 20 m/s strikes a wooden plank and
penetrates up to 20cm. calculate the resistance offered by the wooden plank.
Que.12: A motor car running at the rate of 7 m/s can be stopped by applying brakes in 10m.
Show that the total resistance to the motion, when brakes are on is one fourth of the weight of
the car.
Que.13: A force of 50 N is inclined to the vertical at an angle of 300. Find the acceleration it
produces in a body of mass 2Kg which moves in the horizontal direction
Que.14: A machine gun fires a bullet of mass 40 g with a speed of 1200m/s. the person
holding the gun can exert a maximum fo0rce of 144 N on it. What is the number of bullets
that can be fired from the gun/per second?
Que.15: The initial speed of a body of mass 2 kg is 5 m/s. a force acts for four seconds in the
direction of motion of the body. The force-time graph is shown in fig. calculate the impulse
of the force and final speed of the body.

Que.15: A ball moving with a momentum of 15 kg m/s strikes against the wall at an angle of
300 and if reflected with the same momentum at the same angle. Calculate the impulse.
Que.16: A body of mass 0.25kg moving with velocity 12 m/s is stopped by applying a force
of 0.6N. Calculate the time taken to stop the body. Also calculate the impulse of this force.
Que.17: A glass ball whose mass is 10g falls from a height of 40m and rebounds to a height
of 10 meter. Find the impulse and average force between the glass ball and the floor if the
time during which they are in contact is 0.1s.
Que.18: Two billiard balls of mass 50g moving in opposite directions with speed of 16m/s
collide and rebound with the same speed. What is the impulse imparted by each ball to the
other?
Que.19: Force acting on a body of mass 2kg varies with time as shown in fig. (a) find impulse
of the force and (b) the final velocity of the body. \

Que.20: Fig. shows an estimated force-time graph for a base ball strike by a bat. From this
curve, determine (a) impulse delivered to the ball (b) force exerted on the ball (c) the
maximum force on the ball.
Que.21: A cricket ball of mass 150g moving with a velocity of 15m/s is brought to rest by a
player in 0.05s. Calculate the impulse and average force exerted by the player.
Que.22: A batsman hits back a ball straight in the direction of bowler without changing its
initial speed of 12m/s. if the mass of the ball is 0.15kg; determine the impulse imposed to the
ball. (Assuming linear motion of the ball)
Que.23: An elevator weighing 5000kg is moving upward and tension in the supporting cable
is 50000N. Find the upward acceleration. How far does it rise in a time of 10 seconds starting
from rest?
Que.24: A woman weighing 50kgf stands on a weighing machine placed in a lift. What will
be the reading of the machine, when the lift is (i) moving upwards with uniform velocity of
5m/s and (ii) moving downwards with a uniform acceleration of 1m/s? Take g = 10m/s2.
Que.25: A 75 kg man stands in a lift. What force does the floor exert on him when the
elevator starts moving upwards with an acceleration of 2 m/s? Take g = 10m/s2
Que.26: Find the apparent weight of a man weighing 49 kg on earth when he is standing in a
lift which is (i) rising with an acceleration of 1.2 m/s2 (ii) going down with the same
acceleration (iii) falling freely under the action of gravity and (iv) going up or down with
uniform velocity. Given g = 10m/s2
QUE.27: A bullet of mass 0.01kg and traveling at a speed of 500m/s strikes a block of mass
2kg which is suspended by a string of length 5m. The centre of gravity of the block is found
to rise a vertical distance of 0.1m. What is the speed of the bullet after it emerges from the
block?
Que.28: Two bodies of mass 10kg and 5kg respectively. Calculate the minimum mass of C
which may A stop from slipping. Coefficient of static friction between A and table is 0.2.

QUE.29: When an automobile moving with a speed of 36km/h reaches an upward inclined
road of angle 300, its engine is switched off. If the coefficient of friction involved is 0.1, how
much distance will the automobile move before coming to rest?
QUE.30: Two bodies of mass 10kg and 20kg respectively kept on a smooth, horizontal
surface are tied to the ends of a light string. A horizontal force F= 600N is applied to (1) B,
(2) A along the direction of string. What is the tension in the string in each case?

QUE.31: A body of mass m is moving with speed V collides elastically head-on with
another body of mass m initially at rest. Show that the moving body will come to rest as a
result of this collision.
QUE.32: A 70kg man stands in contact against the wall of a cylindrical drum of radius 3m
rotating about its vertical axis with 200 revolution / minute.
QUE.33: A small object of weight mg hangs from a string of length l. A vertical force F,
which starts at zero and gradually increases is used to pull the object very slowly (so that
equilibrium exists at all the times) until the string makes an angle φ with the vertical.
Calculate the work done by the force F.

QUE.34: in Fig., find the acceleration a of the system and tensions T1 and T2 in the strings.
Assuming that the table and pulleys are frictionless and the strings are mass less.
Given g = 9.8m/s2
QUE.35: Two masses M1 and M2 are connected by a mass less string as shown in fig. Find
the value of tension in string if a force of 200N is applied on (i) M1 and (ii) M2.

QUE.36: Four blocks of the mass m connected by cords are pulled by a force F on a smooth
horizontal surface as shown in fig. determine the tensions T1, T2and T3 in the cords.
QUE.37: Three bodies A, B and C, each of mass m are hanging on a string over a fixed
pulley, as shown in figure. What are the tensions in the strings connecting bodies A to B and
B to C?

QUE.38: In the arrangement shown in fig. Show that the tension in the string between
masses m2 and m2 is: T = (2m1m3g)/(m1 + m2 + m3)
QUE.39: What is the acceleration of the block and the trolley system shown in fig. if the
coefficient of kinetic friction between the trolley and surface is 0.04? What is the tension in
the string? Given g = 10m/s2. Neglect the mass of the string.

QUE.40: In fig. the masses of A and B are of 10kg and 5kg respectively. Calculate the
minimum mass of C which ma stop A from slipping. Coefficient of static friction between A
and table is 0.2.
QUE.41: A block A of mass 14 kg moves along an inclined plane that makes an angle of 300
with horizontal. Bock A is connected to another block B of mass 14kg by a taut mass less
string that runs around a frictionless, mass less pulley. The block B moves downward with
constant velocity. What is (i) the magnitude of frictional force and (ii) the coefficient of
kinetic friction?

QUE.42: When an automobile moving with a speed of 36km/hr reaches an upward inclined
road of angle 300, its engine is switched off. If the coefficient of friction involved is 0.1, how
much distance will the automobile moves before coming to rest? Given g = 10m/s2
QUE.43: A mass of 200 kg is resting on a rough inclined plane of 300. If the coefficient of
friction is 1/√3, find the least and greatest forces acting parallel to the plane to keep the mass
in equilibrium.

QUE.44: Two bodies of mass 2kg and 5 kg are connected by an ideal string passing over a
pulley. The block of mass 2kg is free to slide on a surface inclined at an angle of 300 with
horizontal whereas 5 kg block hangs freely. Find the acceleration of the system and the
tension in the string. Given μ = 0.30