CHAPTER 3 : LAWS OF MOTION

Multiple Choice Questions :

1. A cricket ball (m = 150 g) has an initial velocity ū= ( 3 î + 4 ĵ ) m/s & a final 1
velocity v̄ = – ( 3 î + 4 ĵ ) m/s after being hit. The change in its momentum
(in kg m /s) is
(a) zero (b) – ( 0.45 î + 0.6 ĵ ) (c) – ( 0.9 î + 1.2 ĵ ) (d) – 5 ( î + ĵ )

2. A hockey player moving northward , suddenly turns westward with the same 1
speed to avoid an opponent. The force that acts on the player is
(a) frictional force , westward (b) muscular force , southward
(c) frictional force ,along south – west (d) muscular force , south – west

3. A moving body of mass 2 kg has its position given by x (t) = p t + q t2 + r t3 1

where p = 3 m/s ,q = 4 m/s2 & r = 5 m/s3. The force acting on the body at t = 2s
is
(a) 136 N (b) 134 N (c) 158 N (d) 68 N

4. A body with mass 5 kg is acted upon by a force F = - ( 3î +4ĵ ) N. If its initial 1
velocity at t = 0 is v = (6î - 12ĵ) m/s , the time at which it’ll just have velocity
along the y – axis is
(a) never (b) 10 s (c) 2 s (d) 15 s

5. A point mass m is moved in a vertical circle of radius r with the help of a string. 1
The velocity of the mass is √(7gr) at the lowest point. The tension in the string at
the lowest point is
(a) 1 mg (b) 6 mg (c) 7 mg (d) 8 mg
6. Calculate the acceleration of the block & trolly system if the co – efficient of 1
kinetic friction between the trolly & the surface is 0.05 , mass of the string is
negligible & no other friction exists [ g = 10 m/s2 ]

(a) 1 m/s2 (b) 1.25 m/s2 (c) 1.50 m/s2 (d) 1.66 m/s2

7. Which of the following is a self – adjusting force ? 1

(a) Limiting friction (b) Kinetic friction (c) Static friction (d) All of these

8. A cricketer catches a ball of mass 150 g moving with speed 20 m/s in 0.1 s. He 1
experiences a force of
(a) 300 N (b) 30 N (c)3 N (d) 0.3 N

9. Maximum permissible speed of vehicle along a banked curved road is 1

 (a) v=√ rgtanθ
√
(b) v= rg ( μ+ tanθ
1−μ tanθ ) (c) v=√ μ rg (d) v=
√ r2
tanθ

10 If applied force (F) is less than f s (max ). then static friction ( f s) is given by 1
. (a) f s > F (b) f s < F (c) f s=F (d) f s=2 F

11. Two masses m1 and m2 are attached to a string which passes over a frictionless 1
smooth pulley. When m1  10kg, m2  6kg, a acceleration of masses is

(a) 4 ms−2 (b) 6 ms−2 (c) 8 ms−2 (d) 2.5 ms−2

12 A mass m is suspended from a rigid support P by means of a massless string a 1

. shown . A horizontal force F is applied at point O of the string. The system is in
equilibrium when the string makes an angle  with the vertical. Then the relation
between the tension T, force F and angle  is

(a) F = T sin  (b) F = T cos  (c) (d)

Assertion – Reason Questions :

In the following questions , a statement of assertion (A) is followed by a statement of
reason (R). Mark the correct choice as
(a) Both Assertion (A) & Reason (R) are true & Reason (R) is the correct explanation
of Assertion (A)
(b) Both Assertion (A) & Reason (R) are true but Reason (R) is not 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
(e) Both Assertion (A) & Reason (R) are false
13 Assertion (A) : Ball bearings are commonly used between moving parts of a 1
. machine.
Reason(R) : Ball bearings reduce vibrations & provide better stability

14 Assertion (A) : While taking a turn ,a cyclist leans towards the centre of the 1
. curve while a man sitting in a car leans outwards of the curve.
Reason(R) : An acceleration is acting towards the centre of the curve

15 Assertion (A) : The apparent weight of a body in an elevator accelerating 1

. downwards is less than its actual weight.
Reason(R) : A part of the weight is used to produce downward acceleration .

16 Assertion (A) : The centripetal force & the centrifugal force never cancel out. 1
. Reason(R) : These two forces never act at the same time.

17 Assertion (A) : The centripetal force is always required for motion in a curved 1
. path.
Reason(R) : On a banked track, the vertical component of the normal reaction
provides the necessary centripetal force.

18 Assertion (A) : Two bodies of masses M & m (M > m) are allowed to fall from
. the same height . If the air resistance for each be the same , then
both will reach the earth simultaneously.
Reason(R) : For same air resistance , acceleration of both the bodies will be
same.
Short Answer questions (2 marks) :

19 A 100 kg gun fires a ball of 1 kg horizontally from a cliff of height 500m. If the 2
. ball falls on the ground at a distance of 400m from the bottom of the cliff, find the
recoil velocity of the gun. [ g = 10 m/s2 ]

20 The (x, t) , (y, t) diagram of a particle of mass 500 g , moving in 2 – dimensions is 2

. shown. Find the force (magnitude & direction) acting on the particle.

21 A person in an elevator accelerating upwards with an acceleration of 2 m/s2 , 2

. tosses a coin vertically upwards with a speed of 20 m/s. After how long will the
coin fall back into his hand ? [ g = 10 m/s2 ]

22 A train is accelerating along a horizontal track. If a pendulum suspended from its 2

. roof makes an angle of 4° with the vertical , what is the acceleration of the train ?
[ g = 10 m/s2 ]

Short Answer questions (3 marks) :

23 A helicopter of mass 2000kg rises with a vertical acceleration of 15m/s2. The total 3
. mass of the crew & passengers is 500 kg. What is the magnitude & direction of
(a) the force on the floor of the helicopter by the crew & passengers ?
(b) action of the rotor of the helicopter on the surrounding air ?
(c) the force on the helicopter due to the surrounding air ? [ g = 10 m/s2 ]

24 A rocket has a mass of 2 x 104 kg, half of which is fuel. If the fuel is consumed at 3
. a constant rate as the rocket is fired ,with a constant thrust of 5 x 106 N, calculate
(a) the initial acceleration
(b) the acceleration when the whole fuel is consumed.
[neglect air resistance & any possible variation of g]

Long Answer questions (5 marks) :

25 (a) What is a banked track ? Why & where is it required ? 5

. (b) Using a suitable diagram, derive an expression for the maximum speed with
which a vehicle can take a turn on a banked road.

Case study based questions (4 marks ) :

Projectile motion
A hard blow of a hammer can drive a nail into a wooden block , a ball hitting a wall
bounces back – in both of these cases , a large force acts for a very short duration
producing a finite change of momentum of a body. Though the force & time is difficult to
measure separately , their product known as impulse is measured as the finite change of
momentum. Impulse is a vector quantity , along the direction of force or change of
momentum. For a variable force , impulse is given by the area under the force – time curve.

26 A particle is moving in a circle with uniform speed v. In moving from a point to a 1

. diametrically opposite point , the
(a) momentum changes by mv. (b) momentum changes by 2mv.
(c) kinetic energy changes by ½ mv2. (d) kinetic energy changes by mv2.

27 A ball strikes a bat with velocity v. The ball has mass m & after striking , it 1
. retraces its path. The impulse imparted by the bat is
(a) 3 mv (b) mv (c) zero (d) 2 mv

28 A body , initially at rest on a smooth surface , has a variable force ( as shown in 1

. the graph ) acting on it for 4 s.

The momentum of the ball at the end of 4 s is

(a) 10 Ns (b) 20 Ns (c) 30 Ns (d) 40 Ns

29 Two balls, each of mass 0.06 kg , moving in opposite directions with speed 4 m/s, 1
. collide & rebound with same speed. The impulse imparted to each ball due to the
other is
(a) 0.48 kg m/s (b) 0.81 kg m/s (c) 0.53 kg m/s (d) 0.92 kg m/s

OR

The position – time graph of a particle of mass 0.1 kg is shown 1

The impulse at t = 2 sec is

(a) - 0.2 kg m/s (b) - 0.2 kg m/s (c) 0.1 kg m/s (d) - 0.4 kg m/s