Assignment

(SET - 2)

NEET & AIIMS

(Competitive Entrance Exams.)
82 Laws of Motion Board & Competitive Exams.

8 A body mass 2 kg a constant

SECTION -A of is sliding with
velocity of 4 m/s on a frictionless horizontal table.
Objective Type Questions The force required to keep the body moving with

1 An athiete does not come to rest immediately after the same velocity is

crossing the winning line due to the (1) 8N (2) O N

(1) Inertia of rest (2) Inertia of motion 1
(3) 2 x 10 N (4) N
(3) Inertia of direction (4) None of these
2 When an object is at rest
9 A 10 g moving at 200 m/s stops after
bullet
penetrating 5 cm
of wooden plank. The average
(1) Force is required to keep it in rest state forceexerted on the bullet will be
(2) No force is acting on it
(1) 2000 N (2) -2000 N
(3) A large number of forces may be acting on i
(3) 4000 N (4) -4000 N
which balance each other
10 A mass 50 g is dropped from a height of
ball of
(4) It is in vacuum
20 m. A boy on the ground hits the ball vertically
3
Newton's first law is applicable upwards with a bat with an average force of 200 N,
(1) In all referenceframes so that it attains a vertical height of 45 m. The
time for which the ball remains in contactwith the
(2) Only in inertial referenceframes bat is [Take g=
10 m/s
(3) Only in non-inertial reference frames
(1) 1/20th of a second (2) 1/40 of a second
(4) None of these
(3) 1/80h of a second (4) 1/120th of a second
4. From Newton's second law of motion, it can be
inferred that
11 A on a roof can bear a maximum tension
string tied
of 50 kg The minimum acceleration that can
wt.
(1) No force is required to move a body uniformly be acquired by a man 98 kg to descend will be
along straight line (Take g= 9.8 m/s]
(2) Accelerated motion is always due ar (1) 9.8 m/s? (2) 4.9 m/s?
external force
(3) 4.8 m/s? (4) 5 m/s?
(3) Inertial mass of a body iis equal force
to
required per unit acceleration in the body 12 the object of mass
In the following figure, is held m
at rest by a horizontal force as shown. The force
(4) All of these
exerted by the string on the block is
5 a force of constant magnitude acts in direction
If
perpendicularto the motion of a particle, then its Fixed

(1) Speed is uniform

string
(2) Momentum is uniform

(3) Velocity is unifom object

(m)
(4) of these
6 (1) F (2) mg
When an object is in equilibrium state, then
(1) It must be at rest (3) F+ mg (4) E+m'g²
(2) No force is acting on it 13. In accordance with Newton's third law of motion
(3) Its net acceleration must be zero (1) Action and reaction never balance each other
(4) All of these
(2) For appearance of action and reaction, physical
7 When a force of constant magnitude and a fixed contact is not necessary
direction acts on a moving object, then its path is
(3) This law is applicable whether the bodies are
(1) Circular (2) Parabolic at rest or they are in motion
r
(3) Straight line (4) Either (2)or (3) (4) All of these
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Board & Competitive Exams. Laws of Motion 83
14. When a 4 kg rifle is fired, the 10g bullet receives 20. Tension in the rope at the rigid support is

an acceleration of 3* 10 cm/s. The magnitude =

(g 10 m/s?)
of the force acting on the rifle (in newton) is

(1) Zero (2) 120 60 kg A 2 m/s

(3) 300 (4) 3000
15. A man of mass 50 kg carries a bag of weight
40N on his shoulder. The force with which the floor 50 kg B 2 mvs
pushes up his feet will be
(1) 882 N (2) 530N 40 kg C 1 m's

(3) 90 N (4) 60O N

16 A block of mass m
is released on a smooth inclined

.
(1) 76O N (2) 1360 N
plane of inclination e with the horizontal. The force
exerted by the plane on the block has a magnitude (3) 1580 N (4) 1620 N
21. Two bodies of masses m,and mz ae by
mg et com

d
(1) mg a light string passes over a 1

(<) cose massless pulley. If the pulley is moving upward with

(3) mg tan (4) mg cos
uniform acceleration then tension in the string will
17. In which of the following graphs, the total change be

in momentum is zeo?
m,+m2
+F 3mm2g
()m. + m,
(2)
4m,m,
2g
2m,m,- m,m,
(1) (2) (3)
m, + m, (4) m,+m,
22. In the figure given below, with what acceleration
does the block ofmass m will move? and
st strings are massless and frictionless)
(Pulley

(4)
-2.5

18. A weight Mg is suspended from the middle of a

rope whose ends are at the same level. The rope

is no longer horizontal. The minimum tension m
required
o

completely straighten the rope is

2m
3m
(1) (2) Mg cose

(1)
(3) 2Mg cose (4) Infinitely large
19 Two masses of 10 kg and 20 kg respectively are
connected by a massless spring as shown in fig.
A force of 200 N acts on the 20 kg mass. At the
(3 3
29 (4)

instant shown the 10 kg mass has acceleration 23. T,and T, in the given figure are
12 m/s? towards right. The acceleration of 20 kg
3 kg
5kg 7 kg
mass at this instant is T,
120
200 N
smooth
Smooth surface

(1) 12 ms² (2) 4 m/s² (1) 28 N, 48 N (2) 48 N, 28 N

(3) 10 m/s² (4) Zero (3) 96 N, 56 N (4) 56 N, 96 N

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84 Laws of Motion Board & Competitive Exams.

24. arangement shown,the mass m will ascend

In the 29 Figure shows a uniform rod of length 30cmn having
with an acceleration (Pulley and rope are a mass 3.0 kg. The rod is pulled by constant
massless) forces of 20 N and 32 N as shown. Find the force
(1) Zero
exerted by 20 cm part of the rod on the 10 cm
part (all surfaces are smooth) is

(1) 36N
(2) 12N 20 32 N
(3) g N
10 cm 20 cm

25.
(4) 2g
A uniform rope of mass M and length
tE=
L
2 mg
is fixed at
(3) 64 N
(4) 24 N
itsupper end vertically from a rigid support.Then 30 Mr. A, B and Care trying to put a heavy piston into
the tension in the rope at the distance / from the a cylinderat a mechanical workshop in railway
rigid support is yard. If they apply forcesF.F, and F, respectively
on ropes then for which set of forces at that
(1) Mg L+ (2 M-) instant, they will be able to perform the said job?

Mr. B

(3) Mg (4) Mg

26. A man down a light rope whose breaking

slides
strength n times the weight of man (n < 1). The
is

maximum acceleration of the man so that the rope

just breaks is
Mr.
(1-n) g (1 + n)

,
(1) g (2)
Mr. C
(3) gm (4)
9
27. In the arangement as shown, tension T, is
(1) /3F, -+2F3 (2) 2F, =F, +
(g= 10 m/s?)
(3) 2F, = V3F, (4) Fy =2F,-V3F,
31 In a
rocket, fuel burns at the rate of 2 kg/s. This
fuelgets ejected from the rocket with a velocity of
80 km/s. Forc exerted on is

(1) 16,000 N (2) 1,60,000 N

10 kg
(3) 160O N (4) 16 N
32 A machine gun fires a bullet of mass 65 g with a
(1) 50N (2) 100ON 1300 m/s. The man holding it can exert
velocity of

(3) 50/3N (4) 100V3 N a maximum force of 169 N on the gun. The
number of bullets he can fire per second will be
28. Ifpulleys shown in the diagram are smooth and
massless and a, and a, are ac
acceleration of blocks
(1) 1 (2) 2
of mass 4 kg and kg respectively, then (3) 3 (4) 4
33 A bullet of mass 40 g is fired from a gun of mass
8 kg 10 kg. If velocity of bullet is 400 m/s, then the
(Smooth recoil velocity of the qun will be
surface)

(1)

(3)
,
2a,
= a,
=a,
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(4) a, =4a,
4 kal

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(1)

(2)

(3)

(4)
1.6

1.6

1.8 m/s
m/s in

in
the direction of bullet

m/s opposite to the direction

the direction of bullet

1.8 m/s opposite to the

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direction
of bullet

of bullet
Board & Competitive Exams. Laws of Motion 85
34. A cracker rocket is ejecting gases at a rate of 40. A6 kg bomb at rest explodes into three equal
0.05 ka/s with a velocity 400 m/s. The accelerating pieces P, Q and R. If P flies with speed 30 m/s
force on the rocket is and Q with speed 40 ms making an
angle 90° with
the direction ofP.The angle between the direction
(1) 20 dyne (2) 20N of motion of R
Pand is about
(3) 200ON (4) Zero
(1) 143* (2) 127°
35 A rocket of mass 5700 kg ejects mass at a
constant rate of 15 kg/s with constant speed of (3) 120° (4) 150
12 km/s. The accelerationof the rocket 1 minute 41. A particle of mass 2m moving v
with velocity
after the blast is (g 10 m/s?) = strikes a stationary particle mass 3m and
(1) 34.9 m/s² (2) 27.5 m/s2 sticks to it. The speed of the system will be

(3) 3.50 ms² (4) 13.5 m/s² (1) 0.8v (2) 0.2v
36 A balloon has 2g of
A small hole is pierced
air. into (3) 0.6v (4) 0.4v
it. The air comes
out with a velocity of
42. Which of the following is self-adjusting force?
4 m/s. If the balloon shrinks completely in 2.5 s.
The average forceacting on the balloon is (1) Static friction

(1) 0.008 N (2) Limiting friction

(2) 0.0032 N (3) Kinetic friction

(3) 8N (4) Rolling friction

(4) 3.2 N 43. Maximum force of friction is called

37. If n balls hit elastically and nomally on a surface (1) Limiting friction (2) Static friction
per nit
time and all balls of mass are moving
e
(3) Sliding friction (4) Rolling friction
with same velocity u, then force on surface is

(1) mun (2) 2 mun 44 The limiting friction between two bodies in contact
is independent of

(3) mun (4) mun (1) Nature of the surface in contact

38. A particle of mass m strikes a wall with speed v (2) The area of surfaces in contact
at an angle 30 with the wall elasticaly as shown (3) Normal reaction between the surfaces
in the figure. The magnitude of impulse imparted to

the ball by the wall is (4) The materials of the bodies

45. It is difficult to move a cycle with brakes on because
(1) Rolling friction opposes motion on road
(2) Sliding friction opposes motion on road
(3) Rolling friction is more than sliding friction

mv (4) Sliding friction is more than the rolling friction

(1) mv (2)2 46. Which is a suitable method to decrease friction?

(3) 2mv (4) /3mv (1) Polishing

39. A bomb of mass 1at rest, explodes and

kg initially
(2) Lubrication
breaks into three fragments of masses in the ratio
Ball bearing
1:1: 3 The two pieces of eq
3. equal mass fly off
(3)

perpendicular to eeach other with a speed 15 m/s n (4) All of these

each. The speed of heavier fragment is
47. A cubical block rests on a plane of u= /3. The
(1) 5 m/s angle through which the plane be inclined to the
(2) 15 ms horizontal so that the block just slides down will be

(3) 45 m/s (1) 30° (2) 45°

(4) 5V2 m/s (3) 60° (4) 75

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 86 Laws of Motion Board & Competitive Exams.

48. A block of mass kg is projected from the lowest

1 54. A block of mass m
placed on an inclined plane of
point up along the incdined plane. If g 10 ms2, = angle inclination slides down the plane with

of
the retardation experienced by the block is constant speed.The coefficient of kinetic friction
between block and inclined plane is
(1) sin0 (2) cose
(3) tant (4) cote
Y p=0.5 55. A horizontal force 10 N is necessary to just hold
a block stationary againsta walI. The coefficient of
friction between the block and the wall is 0.2, the
15
a5 ms2 weight of the block

is
(1) ms2 (2)

(3) 610
ms-2 (4) Zero
F=10 N
Wall

49. A child weighing 25 kg slides down a rope hanging

from a branch of a tall tree. If the force of friction
(1) 20 N (2) 50N
acting against him is 200 N, the acceleration of
child is (g =
10 m/s2) (3) 100N (4) 2N
(1) 22.5 m/s² (2) 8 m/s? 56. In the figure shown, the coefficient of static friction
between the block A mass 20 kg and horizontal
(3) 5 m/s? (4) 2 m/s? table is 0.2. What should be the minimum mass of
50 An object of mass 1 kg moving on a horizontal hanging block just beyond which blocks start moving?
surface with initial velocity 8 m/s comes to rest
after 10 s. If one wants to keep the object moving 20 ka
on the same surface with velocity 8 m/s the force
required is
A
(1) 0.4N (2) 0.8 N m0.2
(3) 1.2 N (4) Zero
51. A heavy box is slid across a rough floor with an
initial speed of 4 m/s. It stops moving after (1) 2 kg (2) 3kg
8 seconds. If the average resisting force ction
(3) 4 kg (4) 5kg
is 10 N, the mass of box (in kg) is

(1) 40 (2) 20
57. Two blocks A and B
of masses 5 kg and 3 kg
respectively rest on a smooth horizontal surface
(3) 5 (4) 2.5 with B over A. The coefficient of between A
friction

52 B is 0.5. The maximum rizontal force

If a block moving up an inclined plane at 30° with
(in kg wt.) that can be applied to A, so that there
a velocity of 5 m/s, stops after 0.5 s, then
coefficient of friction will be nearly will be motion of A and B
without relative slipping. is

(1) 1.5 (2) 2.5

(1) 0.5 (2) 0.6

(3) 0.9 (4) 1.1

(3) 4 (4) 5
53. A metallic chain 1m long lies on a horizontal 58. A small metallic sphere of mass is suspended m
surface a table. The chain starts sliding on the from the ceiling of a car accelerating on a horizontal
road with constant acceleration a. The tension in
table if 25cm (or more of it) hangs over the edge
of a table. The correct value of the coefficient of the string attached with metallic sphere is
friction between the table and the chain is (1) mg
1 (2) mg +a)
(1)
3 (2)
(3) m(g- a)
1

(3)
(4) (4) myg? +a
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Board & Competitive Exams. Laws of Motion 87

59. A cyclist riding the bicycle at a speed of SECTION -B

14V3 m/s takes a turn around a circular road of

radius 20/3 m without skidding. What is his Objective Type Questions

inclination to the vertical? 1 A projectile with velocity u at an angle 0
is fired
(1) 30 (2) 45° with horizontal. At the highestpoint of its trajectory
it splits up into three segments of masses m, m
(3) 60 75° nassA with
and 2.m. First part falls verticaly downward
(4)
2
60. A

s
bus a slipperyroad having coefficient of
turns zero initial velocity and second part returns via
fricion of 0.5 with a speed of 10 m/s. The minimum
same path to the point of projection. The velocity
radius of the arc in which bus turns is [Take
g= 10 m/s] ofthird part of mass 2 m
just after explosion will be

(1) 4m (2) 10 m (1) u cos (2)

(3) 15 m (4) 20 m ucos8
61. car is moving a horizontal circular track of radius
A

km with.
with a constant
ona d H
ooeffcient of friction
(3) 2u cos (49 ucose
0.2
etween tyres of car and road is 0.45, then A bomb of mass 9 kg explodes into two pieces of
maximum speed of car may be [Take g 10 m/s] = masses 3
kg and6 kg. The velocity of mass kg 3
(1) 15 m/s (2) 30 m/s is 16 m/s. The kinetic energy of mass 6 kg in

(3) 20 ms (4) 40 m/s joule is

62. A boy is sitting on the horizontal platform of a joy (1) 196 (2) 320
5
wheel at a distance of m from the center. The
(3) 192 (4) 620
wheel begins to rotate and when the angularspeed
exceeds 1 rad/s, the boy just slips. The coefficient 3 In the figure, a ball of mass is tied with two m
of friction between the boy and the wheel is strings of equal length as shown. If the rod is
(g= 10 m/s?) rotated with angular velocity o, then
(1) 0.5 (2) 0.32
(1) 7, > T,
(3) 0.71 (4) 0.2
(2) T, > T,
63. A vehicle is moving on a constant speed
track with
as shown in figure. The apparent weight of the (3) 7, = T, m

vehicle is

(4) 7, =2
6 rod

A 4. A block of wweight 1
1NN rests on an inclined plane
(1) Maximum at A of inclination with the horizontal. The coefficient

(2) Maximum at B of friction between the block and the inclined plane
C is u.The minimum force that has to be applied
(3) Maximum at
parallel to the inclined plane to make the body just
(4) Same at A, B and C move up the plane is

64. A train is running at 20 m/s on a railway line with

radius of curvature 40,000 metres. The distance (1) sin (2) 4 cos
between the two rails is 1.5 mnetres. For safe u cos sin (4) 4 cos + sin

running of train the elevation of outer rail over the

inner rail is (g = 10 m/s) 5 If a pushingforce making an angle a with
(1) 2.0 mm
horizontal applied on a block of mass m placed
is
(2) 1.75 mm on horizontal table and angle of friction is B, then
(3) 1.50 mm (4) 1.25 mm minimum magnitude of force required to move the
65. A car is a horizontal circular road of
moving on block is
radius 0.1 km
constantspeed. If coefficient of
with
friction between tyres of car and road is 0.4,then mgsinfB mg sinß
(1)
speed of car may be (g 10 m/s) = Cos[a -B] (e cos[a + B]
(1) 5 m/s (2) 10 m/s mg sinß mg cosß
(3) (4) cos[a-P)
(3) 20 m/s (4) All of these sin[a+B]

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88 Laws of Motion Board & Competitive Exarms.

6 A 40kg slab rests on a frictionless floor. A 10 kg 11. shown, horizontal forceF,isapplied on

In the figure
block rests on top of the slab. The coefficient of a block but the block does not slide. Then as the
friction between the block and the slab is 0.40.The magnitude of vertical forceF,isincreasedfrom zero
10 kg block is acted upon by a horizontal force of the block begins to slide; the correct statement is
100 N. If g=10 m/s,the resulting acceleration of
slab will be
100 N 10 kg
40 kg (1) The magnitude of normal reaction on block
increases
(1) 1.0 m/s² (2) 1.47 m/s²
(2) Static frictional force acting on the block
(3) 1.52 m/s² (4) 6.1 m/s2 increases
7 A block of mass m, is kept on a wedge of mass M, (3) Maximum value of static frictional force
as shown in figure such that mass remains m decreases
stationary w.r.t. wedge.The magnitude of force Pis
(4) All of these
12 Arrangement of two block system is as shown.The
net force acting on 1 kg and 2 kg blocks are(assuming
the surfaces to be frictionless) respectively

(1) g tan B (2) mg tan B

F=6Nh k 2 kg

(3) (m + Mg tan B (4) mg cot B (1) 4 N, 8 N (2) 1 N, 2 N

8 A particde describes a horizontal circle of radius r (3) 2 N, 4 N (4) 3 N, 6 N
on the smooth surface of an inverted cone as
13. A6000 kg rocket is set for firing. If the exhaust speed
shown. The heightof plane of circle above vertex
is 1000 m/s, how much gas must be ejected each
is h. The speed of particle should be
second to supplythe thrust needed to overcome the
(1) Jg weight the rocket?

(2) /2rg (1) 30 kg (2) 40 kg

(3) 50 kg (4) 60 kg
(3) gh 14. Which of the following is self adjusting force?
(4) J2gh (1) Sliding friction (2) Dynamic friction
If the string of a conical pendulum makes an angle (3) Static friction (4) Limiting friction
9
0 with horizontal, then square of its time period is
15. An open carriage in a goods train is moving with

a
to
proportional
uniform velocity of 10 m/s. If the rain adds water with
(1) sint (2) cos zero velocity atthe rate of 5kg/s, then the additional
force required by the engine maintain the same
(3) tan0 (4) cot0
velocity of the train is
10. Foroe actingona body varies with time asshown below.
If initial momentum of the body is p, then the time (1) 0.5 N (2) 20N
taken by the body to retain its momentump again is (3) 50N (4) Zero
16 A dynamometer D is attached to two blocks of
(in N)
masses6 kg and 4 kg as shown in the figure. The
F reading of the dynamometer is

6kg 4kg

t (sec)
50N € h00000000 3ON
Dynamometer
(1) 8s (2) (4+2/2)s (1) 18 N (2) 28N
(3) 6s (4) Can neverobtain (3) 38 N (4) 48N
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Board Competitive Exams. Laws of Motion 89
17. Figure shows two blocks connected by a light A block of weight Wissupported by three strings as
inextensible string as shown in figure. force of A shown in figure. ch of the following
Which oft relations is
10 N is applied on the bigger block at 60 with true for tension in the strings?(Here T,, T, and T,
horizontal, then the tension in the string connecting are the tension in the strings A,Band C respectively)
the twO masses is
10N

A60 135°
2 kg 3 kg
Smooth surface

(1) 5N (2) 2N (1) T, = T, (2) T,= T,

3N (3) 7, = T, (4) T, = 7,=7,
(3) 1 N
18 22. Acar accelerateson a horizontal road due to force
A block of 10 kg mass is placed on a rough inclined
exertedby
surfaceas shown in figure. The acceleration of the
block will be (1) The engine of the car
(2) The driver of the car
|10k9
(3) The earth as weight of the car
4=1
u-0.8 (4) The road
30
23 Which of the following quantity/quantities aro
(1) Zoro dependent on the choice of orlentation of the
(2) g co-ordinate axes?

(» (4)
3g (a) a+6
2
19 A block (mass =M kg) is placed on a rough incdined (b) 3a, + 2b,
plane. A forceFis applied parallel to the inclined (as (c) (ä +b-)
shown in figure) such that itjust starts moving upward.
The value of Fis (1) Only (b) (2) Both & (b)
(a)

(3) Both (a) & (c) (4) Both (b) & (c)
M 24. The acceleration vector of a particle in unifom circular
motion averaged over the cycleis a null vector. This
statement is
(1) True (2) False
(1) Mg sin 0-pMg cos 0 (2) Mg sin0+ Mg cos0 (3) May be true (4) May be false
(3) Mg sin 0 (4) Mg cos 0 25. Two blocks of mass M
and m are kept on the
20. Figure shows two block system, 4 kg block rests on trolley whose surfaces are smooth select the
al
a smooth horizontal surface,upper surfaceof 4 kg correct statement
is rough. A block of mass 2 kg is placed on its
upper surface.The acceleration of upper blockwith
respect to earth when 4kg mass is pulled by a force
of 30 is F
MA
M m
N,
(1) If F =0blocks cannot remain stationary
f4 kg +30N (2) For one unique value of F. blocks will be
H-0.8 stationary
H-0.6 (3) Blocks cannot be stationary for any value of F
(1) 6 m/s? (2) 5 m/s? because all surfacesare smooth

(3) 8 m/s? (4) 2 /s? (4) Both (1) & (2)

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90 Laws of Motion Board & Competitive Exams.

26. WVhat the acceleration of 3 kg mass when

is 30 A monkey of mass 40 kg climbs up a rope, of
acceleration of 2 kg mass is 2 m/s² as shown? breaking load 600 N hanging froma ceiling. If it
F= 10 N climbs up the rope with the maximum possible
3ka-w2
smooth
kg acceleration,then the time taken by monkey to
climb up is (Length of rope is 10 m]
2 m/s 2s
(1) (2) 1s
(1) 3 ms? 2 m/s (2)

(3) 0.5 m/s2 (4) Zeo

(3) 4s (4) 3s
31. Coefficient of friction between A and B is u. The
27. What is the minimum value of F needed so that
minimum force F with which A will be pushed such
blockbegins to move upward on frictioness incline
plane as shown
that B will not sip down is

M Frictionless

(1)

(3)
Mg tan

Mgsin0
(1+ sin0)
) (2)

4)
Mg

Mg
co

ain
9)

) 32 A
(1)

(3)
Mg

(M+m)g
(2)

(4)

block of mass 10 kg is held at rest against a

mg

(M-m)g

rough vertical wall [u =

0.5] under the action a
28. A force =i+4) acts on the block shown. The force Fas shown in figure. The minimum value of
force of friction acting on the block is
F required for it is (g 10 m/s?) =

|1 kg
=0.3 10 kg

(1) -i (2) -18i

(3) -2.4i (4) -3/

29. Figureshows two cases. In first case a spring (spring (1) 1626 N (2) 89.7 N
constantK)is pulled by two equal and opposite forces 42.7N

FF (3) (4) 95.2 N

Fat both ends and in second case is pulled by a
forceFat one end.Extensions(x) in thespringswill be 33 A block is with speed 20 m/s on a rough
projected
horizontal surface. The coefficient of friction ()
between the surfacesvaries with time (0 as shown
in figure. The speed of body at the end of 4 second
will be (g
F

10 m/s²)
2F
(1) In both cases x
K o.5
(2) In both cases x 0.3+
K

(3) In first case x 2F

in second case x= F
K 2 (S)
,
K

(1) 2 m/s (2) 5m/s

2F
(4) In first case x=in second case x= K (3) 7.2 m/s (4) 9.5 m/s

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Board & Competitive Exams. Laws of Motion 91
34 An object starts from rest and acted upon by a
is 38. An object of mass 2 kg at rest at origin starts
variable force F as shown in If Fo is the
figure. moving under the action of a force
value of the force, then the position of the
initial

object, where it again comes to rest will be -(3i+4)N

F

The velocity of the object at t= 2s will be

(1) (3i + 2)m/s (2) (2i + 4)m/s

(3) (4i+ 4j)m/s (4) (37 -4j) m/s

39. A block of mass m

is at rest on a rough inclined

plane of angle of inclination 6. If coefficient of

2F, friction between the block and the incined plane is
(1) tana (2sinc 4, then the minirmum value of force along the plane
required to move the block on the plane is

(3)
2F (4) mgiucos0 - sino] mgsin0 + ucos0]
cota 2cos a (1) (2)

35. A particle of mass m moves with constant speed (3) mglucos + sinb) (4) mg(sine-ucos)
v on a circular path of radiussras
ras shown in
i figure. 40. A block of mass m takes time t to slide down on a
The average force on it duringi motion om A smooth inclined plane of angle of inclination 0 and
to B is
height h. If same block slids down on a rough
inclined plane of same angle of indination and same
height and takes time n times of initial value, then
coefficient fiction between bock and inclined planeis

(1) (1 + n tan 0 (2)

(3) [1 - tan0 (4)

V3mv my²
(1) (2)
2Tr 41. A person stands in contact against the inner wall of
a rotor of radius r. The coefficient of friction between
2/3mv² 343mv²
(3) (4) the wall and the cothing is and the rotor is rotating
4nr about vertical axis. The minimum angular speed of
36 The frictional force acting on 1 kg block Is the rotor so that the persondoes not slip dowrward

is
u=0.5 H1 kg (1) (2)

100 kg +10 N
(Smooth surface) (3) (4) urg
(1) 0.1 N (2) 2N 42 The magnitude of forceacting on a particle moving
(3) 0.5 N (4) 5N along x-axis varies with time ()as shown in figure.
If at t 0 the velocity of particle is vo, then its
37 The tension T in the string shown figure is
in
velocity at = T, will be

Somi-circle

u=0.7
30e +
Vo
4m (2) 2m
(1) Zero (2) 50N
(3) Vo + 4m (4) V, + m
(3) 35V3N (4) (V3-1) 50 N

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 92 Laws of Motion Board& Conpetitive Exams.

43. Three forces = (2i +4j))N: F: =(2j SECTION -C

and =(k-4i-2j)N are applied on an ob Previous Years Questions
mass 1 kg at rest at origin. The position of the
object at t 2s will be
1 A rigid ball of mnass m strikes a rigid wal at 60
and gets reflected without loss of speed as shown
(1) (-2 m, -6 m) (2) (-4 m, 8 m) in the figure below. The value of impulse imparted

(3) (3 m, 6 m) (4) (2 mn,-3 m) by the wall on the ball will be

44
The momentum p of an object varies with ume () (NEET (Phase-2) 2016]
shown in figure. The corresponding force
(F-time ()graph is

AP (kgm/s) 60
10

(1) mV (2) 2mV

mV mV
2 4 6 8(s) (S)2 (4)3
2 A car is negotiating a curved road of radius R.The
4F(N)
5 road isbanked at an angle 6. The coetficient of

(1)

(2)
o

sfN)
friction

is

(1)

(3)
9 ,
between the tyres of the car and the road
The maxirmum safe velocity on this road is

VR1-4, tan0

1-4,
+lane

(4)
R1
[NEET-2016]

1-4,tan0
tan0
-H,tan0
3 A plank with a box on it at one end is gradually

raised about the other end. As the angle of

inclination with the horizontal reaches 30°,the box
starts to slip and slides 4.0 m
down the plank in
stFN) 4.0 s. The coefficients of static and kinetic friction
between the box and the plank will be, respectively
(3)
(Re-AIPMT-2015]

s1(N) mg

(4)
(1) 0.4 and 0.3 (2) 0.6 and O.6

5
(3) 0.6 and 0.5 (4) 0.5 and 0.6

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Board & CompetitiveExams. Laws of Motion 93
4. Two stones of masses m and 2 m are whirled in
( 9(1-9u) (2)
294
3
horizontal circles, the heavier one in a radius

and lighter one in radius r. The tangential speed of g(1-2u) g(1-24)

lighter stone is n times that of the value of heavier
(3)
3 (4)
2
stone when they experience same centripetal
forces. The value of n is (Re-AIPMT-2015]
The force F acting on a particle of mass is m
indicated by the force-time graph shown below. The
(1) 1 (2) 2 change in momentum of the particle over the time
interval from 0 s to 8 s is [AIPMT-2014]
(3) 3 (4) 4
5. Three blocks A, B and C of masses 4 kg, 2 kg
and kg respectively. are in contact on a
1 6+
frictionless surface, as shown. a force of 14 N If is

applied on the 4 kg block, then the contact force

between Aand is B [AIPMT-2015]

t (s)

(1) 18 N 2N (2) (1) 24 Ns (2) 20 Ns

(3) 6N (4) 8 N (3) 12 Ns (4) 6 Ns
6. A block A of mass m, rests on a horizontal table. 9 A balloon m
descending down with an
with is

A light stringconnected to it passes over a accelerationa (where a < 9). How much mass
frictionless pulley at the edge of table and from its should be removed from it so that it starts moving
other end another block B of mass m, is up with an acceleration a? [AIPMT-2014)
suspended. The coefficient of kinetic friction
between the block and table is When the 2ma
block A is sliding on the table, the tension in the
)g+a
string is [AIPMT-2015]
2ma
m,m, (1-H, 9 (m, +Hm, g
(1) (2)
(m, +m, ) (m, + m,) ma
(3)
g+a
,m,g m,m, (1+ Hg
(3)
(m+m,) (4)
(m, + m,)
(4)
ma

7. A system consists of three masses m,, m,and m, g-a

connected by a string passig over a pulley The P 10. The upper half of an inclined plane of inclination 0
mass mn, hangs freely and m,and m, are on a is perfectly rough. A
smooth while lower half is
rough horizontal table (The coefficient of friction block starting from rest at the top of the plane will
=u). The pulley is frictionless and of negligible again come to rest at the bottom, if the coefficient
mass. The downward acceleration of mass m, is: of friction between the block and lower half of the
(Assume m, = m, = m, = m) [AIPMT-2014] plane is given by NEET-2013]

2
(1) H

tano
(2) 2tane
=
(3) = tano
1
m,
(4) =
tan

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94 Laws of Motion Board & Competitive Exams.

11, Three blocks with masses m, 2m and 3m are 15. A person of mass 60 kg is inside a lift of mass
connected by strings, as shown in the figure. After 940 kg and presses the button on control panel.
an upward force F is applied on block m, the The lift starts moving upwards with an acceleration
masses move upward at constant speed v. What 1 m/s². If g = 10 ms2, the tension in the
is the net force on the block of mass 2m? (g is supporting cable is [AIPMT (Prelims)-2011]
the acceleration due to gravity) NEET-20131 (1) 1200 N (2) 8600 N
(3) 9680 N (4) 11000 N
16 A body of mass M hits nomally a rigid wall with
m
velocity v and bounces back with the same
velocity. The impulse experienced by the body is
2m [AIPMT (Prelims)-2011)

3m (1) Zero (2) Mv

(3) 1.5MV (4) 2MN
(1) 2mg (2) 3mg 17. A radioactive nucleus of mass emits a photon of M
(3) Gmg (4) Zeo frequency v and the nuceus recoils. The recoil
energy will be: [AIPMT (Prelims)-2011]
12. An explosion breaks a rock into three parts in a
horizontal plane. Two of them go off at right angles (1) hv (2) Mo- hy
to each other. the first part of mass 1 kg moves
a speed of 12 ms and the second part of (3) (4) Zero
with 2Me?
mass 2 kg moves with 8 ms-1 speed. If the third 18 A block of mass m is in contact with the cart C as
part flies off with 4 ms speed, then its mass is
shown in the figure.
[NEET-2013]

(1) 5 kg (2) 7kg

(3) 17 kg (4) 3 kg VI m
13. Acarof mass 1000 kg negotiates a banked curve
of radius 90 m on a frictionless road. If the banking
angle

(1)

(2)
is

5 ms-1
10 ms-1
45", the speed of the car is

(AIPMT (Prelims)-2012] The

and
that
the cart is .
coefficient of static between the block
friction

The acceleration u off the cart

will prevent the block from faling satisfies:

[AIPMT (Prelims)-2010]
(3) 20 ms-1
30 ms-1 a > mg

,
(4) (1)

14. A car of mass mmoving on a level circular track

is

of radius R. represents the static friction

If

between the road and tyres of the car, the (2) u > um 9
maximum speed of the car in circular motion is
givenby [AIPMT (Mains)-2012]

Rg az
(1) Ju,mRg (2) . (3)

(4) ,Rg (4) a<

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Board & CompetitiveExams. Laws of Motion 95
19. A gramophone record is revolving with an angular 24. A roller coaster is designed such that riders
velocity o. A coin is placed at a distancerfrom the experience "weightessness" as they go round the
centre of the record. The static coefficient of fricion top of a hill whose radius of curvature is 20 m. The

is u. The coin will revolve with the record if: speed of the car at the top of the hill is between
[AIPMT (Prelims)-2010] (AIPMT (Prelims)-2008]
(1) 13 m/s and 14 m/s
(1) r ugu (2) r<
(2) 14 m/s and 15 m/s
Ag
r< (4) r
(3) 15 m/s and 16 m/s
(3)

20. A body, under the action of a force (4) 16 m/s and 17m/s
25 A block B
is pushed momentarily along a
F =6i-8j + 10k, acquires an acceleration of
horizontal surface with an initial velocity v. If is
1 m/s², The mass of this body must be: the coefficient of sliding friction between B and the
[AIPMT (Prellms)-2009] surface,block B will come to rest after a time
(1) 10 kg (2) 20 kg
(3) 10/2kg (4) 2/1O kg
21. The mass of a lift is 2000 kg. When the tension in
the supporting cable is 28000 N, then its
accelerationis: [AIPMT (Prellms)-2009] [AIPMT (Prelims)-20071
(1) 4 ms² upwards (2) 4 ms- downwards
(3) 14 ms2 upwards (4) 30 ms² downwards (2)
22. Sand is being dropped on a conveyor belt at the rate
of M kg/s. The force ay to keep the
we
belt

moving with a constant y of v m/e will be

(3) (4)
V V
(AIPMT (Prellms)-2008]
(1) Zero (2) Mv newton 26. A 0.5 kg ball moving with a speed of 12 m/s strikes
a hard wall at an angle of 30 with the wall. is
Mv It

(3) 2M newton (4) newon reflected with the same speed and at the same
angle. If the ball is in contact with the wall for
23. Three forces acting on a body are shown in the
0.25 s, the average force acting on the wall is:
figure. To have the resultant force only along the
y-direction, the magnitude of the minimum
additional force needed is

[AIPMT (Prelims)-2008]
4N
1N

[AIPMT (Prelims)-2006]
(1) V3 N (2) 0.5 N
(1) 48 N (2) 24 N
(3) 1.5 N (3) 12 N (4) 96 N
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96 Laws of Motion Board & Competitive Exams.

27. A tube of length L completely with an

is filled
31 An object is moving on a plane surface uniform
incompressible liquid of mass

the liquid at the other end is

.
and ciosed at
both the ends. The tube is then rotated in a
horizontal plane about one of its ends with a
uniform angular velocity
M

The force exerted by

[AIPMT (Prelims)-2006] 32
velocity 10 ms-1 in presence of a force 10 N.
The frictional force between the object and the
surface is

(1)

(3)
1N
10 N
A body of mass M
(2) -10
(4)

starts sliding
100ON
N

down on the
inclined plane where the angle is
(1)
2
MLu ZACB
kinetic
= 30
friction
as shown
will be
in figure.
critical
The coefficient of

(2)
2
ML
30
(3) MLu?

ML'u
(4)
2
28. A conveyor moving at a constant speed of (2) V3Mg
belt is V3
2 m/s. A box is gently dropped on it. The
coefficient of friction between them is u 0.5. The = (3) J3 (4)) None of these
distance that the box will move relative to belt
before coming to rest on it, taking g= 10 ms2, is 33 In non-inertial frame, the second aw of motion is
written as
[AIPMT (Mains)-2011]
(2) 0.4 m
(1) F= ma (2) F ma +F.
(1) Zero
(3) F= ma F (4) F 2ma
(3) 1.2 m (4) 0.6 m
whereF, is a pseudo-force whlle a is the
Questionsasked Prior to Medical Ent. Exams. 2005 acceleration of the body relative to non-inertial
29. A stone is dropped from a height h. It hits the frame.
ground with a certain momentum P. If the same
34. A person a rifle (mass of person and rifle
holding
stone is dropped from a height 100% more than
together 100 kg) stands on a smooth surface
is
the previous height, the momentum when it hits
the ground will change by
and fires 10 shots horlzontally, in s. Each bullet 5
has a mass of 10 g with a amuzzle velocity of 800
(1) 68% ms-, The final velocity acquiredby the person and
(2) 41% the average forceexerted on the person are

(3) 200% (1) -1.6 ms-1; 8 N

(4) 100% (2) -0.08 ms1: 16 N

30. A mass m moving horizontally (along the x-axis) (3) -0.8 ms1: 16 N
with velocity v collidesand sticks to a mass of 3m (4) 1.6 ms-1: 16 N
moving vertically upward (along the y-axis) with
velocity 2v. The final velocity of the combination is 35. In a burns at the rate of 1 kg/s. This
rocket, fuel
fuel is ejectedfrom the rocket witha velocity of
60 km/s. This exerts a force on the rocket equal
to

(1) 6000 N (2) 60000 N

(3) (4)

(3) 60 N (4) 600N

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Board & CompetitiveExams, Laws of Motion 97
36. A satellite in force-free space sweeps stationary 42. A from a gun.The force on the bullet
bullet is fired
interplanetary dust at a rate of dMidt av,where = isgiven by F =
600- 2 x 105 t, whereF is in
M is mass and v is the speed of satellite and newton and t in second. The force on the bullet
is a constant. The tangential acceleration of becomes zero as soon as it leaves the barrel.
satellite is What is the impulse imparted to the bullet?

(1) 9 Ns (2) Zero

(1)
2M (2) -ay² (3) 1.8 Ns (4) 0.9 Ns
43 A ball of mass 0.25 kg attached to the end of a
-2ov² -CAV
string of length 1.96 m is moving in a horizontal
(4)
(3)
M The string will break if the tension is more
circle,
than 25 N. What is the maximum speed with
37. A man fires a bullet of mass 200 gm at a speed which the ball can be moved?
of 5 m/s. The gun is ofone kg mass. By what (1) 5m/s (2) 3m/s
velocity thegun rebounds backward?
(3) 14 m/s (4) 3.92 m/s
(1) 1 m/s (2) 0.01 m/s 44 A mass of 1 kg is suspended by a thread. It is

(3) 0,1 m/s (4) 10 m/s (i) lifted up with an acceleration 4.9 m/s?, (ii)
lowered with an acceleration 4.9 m/s?. The ratio of
38. A 10 N force is appliedon a body produces in it an
the tensions is
acceleration of 1 m/s2.The mass of the body is

(1) 1:3 (2) 1:2

(1) 15 kg (2) 20 kg
(3) 3: (4) 2:1
5 kg9

1
(3) 10 kg (4)
46 Ifthe forceon a rocket, that releases the exhaust
39. A force of 6 N acts on a body at rest and of mass
gases with a velocity of 300 m/s is 210 N, then
kg. During this time, the body attains a velocity the rate of combustion of the fuel is
of 30 m/s. The time for which the force acts on the
body is (1) 0.07 kg/s (2) 1.4 kg/s

(1) 7 second (2) 5second (3) 0.7 kg/s (4) 10.7 kg/s

(3) 10 second (4) 8 second 46 A 500 kg car takes a round turn of radius 50 m
with a velocity of kmvh. The centripetal force is
40. A shell, in explodes into four unequal
flight, parts.
Which of the following is conserved? (1) 1000 N (2) 750 N
(1) Potential energy (3) 250N (4) 1200 N

(2) Momentum 47 Two masses as shown are suspended from a

massless Calculatethe acceleration of the
pulley.
(3) Kinetic energy
10 kg mass when masses are left free
(4) Both (1) & (3)
41. A 5000 kg rocket is set for vertical firing. The
exhaust speed is 800 ms-1. To give an initial
upward accelerationof 20 ms-2, the amount of
gas ejected per second to supply the needed 5 kg
10 kg
thrust wll be (g= 10 ms )

(1) 185.5 kg s-1

(2)
(2) 187.5 kg s

(3) 127.5 kg s
(3) (4)
(4) 137.5 kg s

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98 Laws of Motion Board & Competitive Exarns.

48. A mass of 1 kg is thrown up with a velocity of 53 An object of mass 3 kg is at rest. Now a force
100 m/s. After 5 second, it explodes into two F =61i+4j is applied on the object then
parts. One part of mass 400 g moves down with
a velocity 25 m/s. Calculate the velocity of other velocity of object at t= 3s is
part just after the explosion.(g = 10 ms2) (1) 18i + 3) (2) 187 +6j
(1) 40 m/s (2) 40 m/s I (3) 3i + 18j (4) 18/ +4j
(3) 100 m/s T
(4) 60 m/s T 54 A block of mass 10 kg placed on rough horizontal
49. A man on a frictionless inclined plane
is slipping surface having coefficient of friction 0.5, if a =
and a bag falls down from the same height. Then horizontal force of 100 N is acting on it then
the velocity of both is related as velocity of (V= acceleration of the block will be (g 10 ms-2) =
bag and V
velocity of man)
(1) 10 m/s? (2) 5m/s?
(1) V> Vm (3) 15 m/s? (4) 0.5 m/s?
(2) V< Vm 55 A lift of mass 1000 kg is moving with acceleration
(3) V = Vm of m/s?
1 in upward direction, then the tension

(4) V and V can't be related

developed in string which is connected to lift is

50. A body mass 3 kg moving with velocity 10

of m (1) 9800 N (2) 10,800 N

s hits a wall at an angle of 60

and returns at the (3) 11,000 N (4) 10,000 N
same angle. The impact time was 0.2 s. Calculate 56 A monkey of mass 20 kg is
a vertical rope.
holdingg
the force exerted on the wall.
The rope will not break when a mass of 25 kg is
suspended from but will break if the mass
it

exceeds 25 kg. What is the maximum

accelerationwith which themonkey can climb up
60 along the rope? (g 10 m/s?) =
60° (1) 5 ms² (2) 10 m/s²
(3) 25 m/s² (4) 2.5 m/s?
57. A man weighs 80 kg. He stands on a weighing
scale in a lift which is moving upwards with a
(1)) 150,J3 N (2) 50 J3 N uniform acceleration of 5
m/s². What would be the

(3) 10ON (4) 75 N

reading on the scale? (g = 10 m/s?)
(1) Zero (2) 40O N
51. A cricketer catches a ball of mass 150 in g
0.1 s moving with speed 20 m/s, then he (3) 800N (4) 1200 N
experiences force of 68 The coefficient of static function, (,)between
(1) 300 N (2) 30 N block A of mass 2 kg and the table as shown in
the figure is 0.2. What would be the maximum
(3) 3N (4) 0.3 N mass value of block B so that thetwo blocks do
52. On the surface of a truck, a block of
horizontal not move? (The string and the pulley are
mass 1 kg is =
placed (u 0.6) and truck is moving assumed to be smooth and massless)
with acceleration 5
m/s² then the frictional force
on the block will be
2kg A
(1) 5N
(2) 6N
(3) 5.88 N
(4) 8N B|
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Board & Competitive Exams. Laws of Motion 99
(1) 2.0 kg (2) 4.0 kg 1. A: Due to inertia an object is unable to change
by itsef its state of rest and uniform motion.
(3) 0.2 kg (4) 0.4 kg

59. A block of mass m placed on a smooth wedge

is
R: An object cannot change its state unless
of inclination 0.The whole system is accelerated acted upon by an unbalanced external force.
horizontally so that the block does not slip on the 2. A: Acceleration of an object in uniform motion is
wedge. The force exerted by the wedge on the zero.
block (g is acceleration due to gravity) will be
R:No forceis required to move an objet unifornly
(1) mgcose
3. A: Newton's second law of motion gives the
(2) mgsin0 measurement of force.

(3) mg R: According to second law of motion, force is

(4) mglcos) directly proportional to the rate of
of c
change of
momentum.
60 A car is moving in a circular horizontal track of
radius 10 m a
constant speed of 10 m/s. A
with 4. A: According to Newton's third law of motion for
bob is suspended from the roof of the car by a light every action, there is an equal and opposite
wire of length 1.0 m. The angle made by the wire reaction.
with the vertical is
R: There is no time lag between action and
reaction.
(1)0P (2)
5. A:Inetia depends on the mass of an object.

R:Greater the mass, larger is the force required

(3) & (4) to change its state of rest or of uniform
motion
61 A man of 50 kg mass is standing in a gravity free 6, A:In case of free fall of a lift, the apparent weight
space at a height of 10 m above the floor. He of a man in it will be zero.
throws a stone of 0.5 kg mass downwards with a
speed 2 m/s. When the stone reaches the floor, R:In free fall, acceleration of lift is equal to
the distance of the man above the floor will be acceleration due to gravity.
(1) 20 m (2) 9.9 m 7. A: Static friction force is a self adjusting force.

(3) 10.1 m (4) 10 m R: The interatomic forces at the point of contact

give rise between the surfaces.
SECTION -D to friction

8 A The value of kinetic friction is less than the

Assertion-Reason Type Questions limiting friction.

Inthe following questions,a statementof assertion (A)is R:When motion of an object started, the inertia
followedby a statement of reason (R).
of rest has been overcome.
(1) If both & Reason are true and the
Assertion
reason the correct explanation of the
is
9. A:During horizontal circular turn of a car, the
centripetal force required should be less than
assertion,then mark (1).
the limiting friction between its tyres and road.
(2) Ifboth Assertion & Reason are true but the
reason is not the correct explanation of the R: The centripetal force to car is provided by the
assertion,then mark (2). frictional force between its tyres and the road.

(3) IfAssertion is true statement but Reason is

10. A A person on a frictionless surfacecan get away
false, then mark (3). from it by blowing air out of his mouth.

(4) Ifboth Assertion and Reason are false R: For every action there is an equal and opposite
statements,then mark (4). reaction.

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100 Laws of Motion Board & Competitive Exams.

11. A: It isdifficult to move a cycle along a road with R: By banking of the roads,one component of the
its brakes on. normal reaction on the automobile contributes
to necessary centripetal force.
R:Sliding friction is greaterthan rolling friction.
14. A: The centripetal and centrifugal forces never
12. A: It makes walk on slippery muddy road
easier to
cancel each other.

if we throw some sand on R: They are action and reaction forces.

it.
R:On throwing sand, frictional force of the surface 15. A: Work done by friction can increasethe kinetic
increases energy of the body.

13. A: Banking of roads reduces the wear and tear of

R:Friction is a type of and it always
contact force
opposes the relative motion or tendency of
the tyres of automobiles. relatlve motion,

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