Objective Questions

Single Correct Option

1. Two balls A and Bof same size áre dropped from the same point under gravity. The mass of Ai
greater than that of B. If the air resistance acting on each ball is same, then
(a) both the balls reach the ground simultaneously
(b) the ball A reaches earlier
(c) the ball B reaches earlier
(d) nothing can be said
2. Ablock of mass mis placed at rest on an inclined plane of inclination to the horizontal. Ite
coefficient of friction between the block and the plane is , then the total force, the inclina
plane exerts on the block is
(a) mg (b) | mg cos 0
(c) mg sin 0 (d) u mg tan 0
3. In the figure, a block of mass 10 kg is in equilibrium. Identify the string in which the tension a
zero.

30,

C
A

10 kg
(a) B (b) C (c) A (d) None of these
-n
4. At what minimum acceleration should a monkey slide a rope whose breaking strengthis3
its weight ?
(a) 28
3
(b) g (c) (d) zero

5. For the arrangement shown in the figure, the reading of spring

balance is
(a) 50 N
(b) 100 N
(c) 150 N 10
KgL

(d) None of the above 5 kg

 Chapter 8 Laws of Motion 373

The timetaken by a body to slide down a rough 45° inclined plane is twice that required to sinae
down asmooth 45° inclined plane. The coefficient of kinetic friction between the object and
rough plane is given by
1 3
4

7.Aforce accelerates a particle from rest to avelocity u. Another force F, decelerates the same
particle from vto rest, then
(a) F is always equal to F,
(b) F, is greater than F,
(c) F, may be smaller than, greater than or equal to F
(d) F, cannot be equal to F
friction
8. A particle is placed at rest inside a hollow hemisphere of. radius R. The coefficient of
1
between the particle and the hemisphere is u = The maximum height up to which the

particle can remain stationary is

R
(a)
2
3R
(C) R
(d)
2

figure shown, the frictional coefficient between table and block is 0.2. Find the ratio of
9. In the
tensions in the right and left strings.
5kg

5kg

|15kg
(b) 34 :12
(a) 17:24 (d) 3: 2
(c) 2:3 the horizontal is inside s lie
having inclination with
a Smooth inclined nlane of length L taken by a body to slide down the
incined
retardation a. The time
wnich is moving down with a
plane from rest will be 2L
2L (b) V(g- a) sin
(a)
V(g+ a) sin 0 2L
(d) Vgsin 0
(c) 2L
a sin
making an angle of 30° with horizontal. The coefficient
1. A inclined plane Ift
block rests on a rough block and inclined plane is 0.8. the frictional force on the block is
of static between the m/s)
friction kg) is(Take, g= 10
10 N, the of the block
mass (in (b) 4.0
(a) 2.0 (d) 2.5
(c) 1.6
374 " Mechanics - I

12. In figure, two identical particles each of mass m are tied together with an inextensible gtring
This is pulled at its centre with a constant force F. If the whole system lies on a smooth
horizontal plane, then the acceleration of each particle towards each other 18

30°
’F
30°

F (b)l
(a)
2 m 2/3 m
2 F
(c)
V3 m
13. Ablock of mass 4 kg is placed on a rough horizontal plane. Atime dependent horizontalforce
F- kt acts on the block. Here k= 2 Ns, The frictional force between the block and plane at
time t=2s is (u = 0.2)
(a) 4 N (b) 8 N (c) 12N (d) 10N
14. A man of mass m slides down along a rope which is connected to the ceiling of an elevator with
deceleration arelative to the rope. If the elevator is going upward with an acceleration a
relative to the ground, then tension in the rope is
(a) mg (b) m(g + 2a) (c) m(g t a) (d) zero

15. A 50 kg person stands on a 25 kg platform. He pulls on the rope which is attached to the
platform via the frictionless pulleys as shown in the figure. The platform moves upwards at a
steady rate, if the force with which the person pulls the rope is

(a) 500 N (b) 250 N

(c) 25 N (d) None of these
16. If a ladder weighing 250 N is placed against a smooth vertical wall having coefficient af friction
between it and floor 0.3, then what is the maximum force of friction available at the point ot
contact between the ladder and the floor?
(a) 75 N (b) 50 N (c) 35 N (d) 25 N
17. A rope of length L and mass M is being pulled on a rough horizontal floor by a constant
horizontal force F= Mg. The force is acting at one end of the rope in the same direction as the
length of the rope. The coefficient of kinetic friction between rope and floor is 1/2. Then, the
tension at the mid-point of the rope is
(a)
Mg (b) 2Mg
4 5

(c) Mg (d) Mg
8 2
 375
Chapter 8 Laws of Motion
block Aof mass 4 kg is kept on ground. The coefficient of friction between the block and the
18. A
ground is 0.8. The external force of magnitude 30 Nis applied parallel to the ground. The
Pesultant force exerted by the ground on the block is (g = 10 m/s²)
(a)40N (b) 30 N
(c) zero (d) 50 N
block Aof mass ZKg rests on another block Bof mass 8 kg which rests on a horizontal flo0r.
49. A 0.5. When a
The coefficient of friction between Aand Bis 0.2 while that between Band floor is
horizontal force F of 25 Nis applied on the block Bthe force of friction between Aand B18
(a) 3 N (b) 4 N
(c) 2 N (d) zero
with the
20. A body of mass 10 kg lies on a rough incined plane of inclination =sin
horizontal. When the force of 30 N is applied on the block parallel to and upward the plane, the
total force by the plane on the block is nearly along
A B
30N

mmanmmmmm

(a)OA (b) OB (c) OC (d) OD

21. In the figure shown, a person wants to raise a block lying on the ground to a height h. In which
case, he has to exert more force. Assume pulleys and strings are light

() (i)

(a) Fig. () (b) Fig. (i)

(c) Same in both (d) Cannot be determined
22, Aman of mas8 mstands on a platform of equal mass m and pulls himself by two ropes passing
Over pulleys as shown in figure. If he pulls each rope with a force equal to half his weight. his
upward acceleration would be

(a) & (c) g (d) zero

2 (o)
376 Mechanics - I
23. Avarying horizontal force F= at acts on a block of mass mkept on asmooth horizontal
lo\cksSuriacies.y.
An identical block is kept on the first block. The coefficient of friction between the
The time after which the relative sliding between the blocks prevails 1s
(a) mg mg
(b) 2umg (c) (d) 2u mga
24. Two particles start together from apoint Oand slide down along straight smooth
at 30° and 60° to the vertical plane and on the same side of vertical through )
wires inclined
acceleration of second with respect to first will be of magnitude The relative
(a) (c)& (d) g
2
25. In the arrangement shown in the figure, the pulley has a mass 3m. Neglecting friction on t.
contact srface, the force exerted by the supporting rope AB on the ceiling is
A
LLLLLLLLLLL

m
2m
(a) 6 mg (b) 3 mg (c) 4 mg (d) None of these
26. If a body loses half of its velocity on penetrating 3 cm in a wooden block, then how much willit
penetrate more before coming to rest?
(a) lcm (b) 2 cm
(c) 3 cm (d) 4 cm
27. A weightless rod is acted upon by upward parallel forces of 4 N and 2 N magnitudes at ends A
and B respectively. The total length of therod AB= 3 m. To keep therod in eguilibrium a force
of 6N should act in the following manner
(a) downward at any point between A and B
(b) downward at the mid-point of AB
(c) downward at a point Csuch that AC =1m
(d) downward ata point C such that BC = 1 m
28. Ametal sphere is hung by a string fixed to a wall. The forces acting on the sphere are shown in
figure. Which of the following statements is correct?

’R

(i) R T+ w =0 (ii)T² = R+ w
(iii) T = R+ w (iv) R= w tan 0
(a) (i), (iü), (ii) (b) (ii), (i), (iv)
(c) (i), (i), (iv) (d) (i), (ii), (ii), (iv)