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M m

A

B

R1 R2

O

90o

PHYSICS TEST

FRICTION

1. A block of mass m = 1 kg placed on top of another block of mass M = 5 kg is attached to a horizontal spring of force constant K = 20 N/m as shown in figure. The coefficient of friction between the blocks is whereas the lower block slides on a frictionless surface. The amplitude of oscillation is 0.4 m. What is the minimum value of such that the upper block does not slip over the lower block?

A) 0.133 B) 0.5 C) 0.362 D) 0.21 2. Block A is placed on a smooth horizontal surface. Another block B is placed in contact

with A as shown in figure. The coefficient of friction between A and B is 0.5. The minimum acceleration of block A so that block B does not fall

A) 10 m/s2 B) 20 m/s2 C) 15 m/s2 D) 5 m/s2 3. A block of mass m is pulled along a horizontal surface by applying a force at an angle

with the horizontal. The friction coefficient between the block and the surface is . If the block travels at a uniform velocity then calculate the work done during its displacement d.

A) mgdcos

B)

sinmgd

C) mgdcos sin

D) mgdcos sin

4. A uniform chain of length and mass m overhangs from a smooth table so that 2/3rd

part of it is on the table. If the coefficient of friction is , then for the equilibrium of the chain, find .

A) 0.5 B) 0.75

C) 0.25 D) None of these 5. A block of mass 'm' is sliding on an inclined right angle trough as shown in figure (a)

and (b). If is the coefficient of kinetic friction then the acceleration of the block is Fig (a) Fig (b) A)

B)

C) D) 6. The magnitude of frictional forces between the blocks 'A' and 'B' and between 'B' and

the horizontal surface is (g = 10 m/s2) A) 90N, 5N B) 0N, 75N C) 0N, 80N D) 5N, 75N

g sin cos

g sin cos2

g sin 2 cos

g sin 2 cos

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7. A long wooden plank of length 9 m is resting on a horizontal surface. A small block of

mass 2 kg is resting at the center of the plank. The coefficient of friction between the block and the plank is 0.3. If the plank is pulled forward in the direction of its length by a horizontal force with an acceleration of 4 m/s2, then the time taken by the block to leave the plank is ( g = 10 ms-2 )

A) 2 sec B) 4 sec C) 3 sec D) 6 sec 8. The force applied on a body on a rough surface produces acceleration a. If the

coefficient of friction between the body and the surface is reduced to3 , the

acceleration increases by 2 units, the value of is

A) 23g

B) 32g

C) 3g

D) 1g

9. A body takes n times as much time to slide down an identical 450 rough incline as it takes to slide down a smooth 450 incline. The coefficient of friction of rough incline is

A) 211n

B) 21

1 n C) 2

11n

D) 2

11 n

10. The coefficient of friction between a hemispherical bowl and an insect is 0.44 and the radius of the bowl is 0.6 m. The maximum height to which an insect can crawl in the bowl will be

A) 0.4 m B) 0.2 m C) 0.3 m D) 0.1 m 11. A block slides down a rough inclined plane of slope angle ' ' with a constant velocity.

It is then projected up the same plane with an initial velocity . The distance traveled by the block up the plane before coming to rest is

A) 2

4 sing

B)

2

2 sing

C)

2

sing

D)

2

sin

12. A body slides down a rough inclined plane of inclination with constant velocity . If it is projected up the inclined with velocity 2 , then it moves up the plane with

A) constant velocity B) retardation g sin C) retardation 2g sin D) acceleration g sin 13. A block of mass m is pressed against a vertical wall by applying force p at an angle

to the horizontal as shown. As a result, if that block is prevented from falling down and is coefficient of static friction between the block and the wall, the value of P is

A) sin cos

mg

B) sin cos

mg

C) cos sin

mg

D) cos sin

mg

14. A 4kg slab rest on a frictionless floor. A 20 kg block rests on the top of the slab. The

between the block and slab is 0.6 What is the maximum value of force F so that both slab and block will remain at rest relatively ( g = 10m/s2)

A) 120N B) 240N C) 720N D) 200N

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15. Two blocks of mass 4kg and 2kg are placed side by side on rough horizontal surface as

shown in Fig. A horizontal force of 20N is applied on 4kg block and between horizontal surface and both the block is 0.2, the force applied by 4kg block on 2kg block.

A) is more if 0 B) is less if 0 C) will remain same if 0 D) none of these

16. In the arrangement shown in figure, coefficient of friction between the two blocks 12

. The force of friction acting between the two blocks is: A) 8N B) 10N C) 6N D) 4N 17. A block A of mass m is placed over a plank B of mass 2m. Plank B is placed over a

smooth horizontal surface. The coefficient of friction between A and B is 12

. Block A is

given a velocity v0 towards right. Acceleration of B relative to A is:

A) 2g

B) g

C) 34g D) zero

18. A wedge of mass 2m and a cube of mass m are shown in figure. Between cube and wedge, there is no friction. The minimum coefficient of friction between wedge and ground so that wedge does not move is

A) 0.10 B) 0.20 C) 0.25 D) 0.50 19. The minimum acceleration (from the given option) that must be imparted to the car in

the figure so that the block A will not fall (given 0.2 is the coefficient of friction between the surfaces of block and cart) is given by

A) 25 m/s2 B) 5 m/s2 C) 5.4 m/s2 D) 49 m/s2 20. A block is placed over a plank. The coefficient of friction between the block and the

plank is 0.2 . Initially both are at rest, suddenly the plank starts moving with acceleration 20 4 /a m s . The displacement of the block is 1S is (g= 10 m/s

2) A) 1m relative to ground B) 2m relative to plank C) zero relative to plank D) 2m relative to ground. 21. A block of mass 2kg rests on a rough inclined plane making an angle 300 with the

horizontal the s between the block and plane is 0.7. The frictional force on the block is A) 9.8N B) 0.7 x 9.8 x 3 N C) 9.8 3 N D) 0.7 x 9.8N 22. Block of mass 0.1 kg is held against a wall applying a horizontal force of 5N on the

block, if the between block and wall is 0.5, the magnitude of frictional force acting on the block is

A) 2.5N B) 0.98 N C) 4.9 N D) 0.49N

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23. How much should the angle of an inclined plane be so that a mass of 2 kg be stationary?

Given s = 1/3 and k = 1/3. A) 300 B) 600 C) 450 D) None 24. A 10kg block is released from point A in the figure. The track is frictionless except for

the portion between points B and C, which has a length of 6.00 m. The block travels down the track hits a spring of force constant 2250 N/m, and compresses the spring 0.300 m from its equilibrium position before coming to rest momentarily. The coefficient of kinetic friction between the block and the rough surface between B and C is

A) k 0.73 B) k 0.33 C) k 0.83 D) k 0.13 25. A 2.00 kg block situated on a rough incline is connected to a

spring of negligible mass having a spring constant of 100 N/m. The pulley is frictionless. The block is released from rest when the spring is unstretched. The block moves 20.0 cm down the incline before coming to rest. The coefficient of kinetic friction between block and incline is

A) 0.615 B) 0.515 C) 0.115 D) 0.315 26. A heavy block of mass M is slowly placed on a conveyer belt moving with a speed v.

The coefficient of friction between the block and the belt is . Through what distance will the block slide on the belt?

A) vg

B) 2vg

C) v2 g

D) 2v

2 g

27. A uniform rope of length l lies on a table. If the coefficient of friction is , then the maximum length l of the part of this rope which can overhang from the edge of the table without sliding down is

A) l

B) 1

l

C) D)

28. The minimum acceleration that must be imparted to the cart in the figure so that the block A will not fall (given is the coefficient of friction between surface of the block and the cart) is given by.

A) g B) g

C) g D)

g

29. A particle is projected along the line of greatest slope up a rough plane inclined at an angle of 45 with horizontal. If the coefficient of friction is 1/2, then retardation is

A) 22

g B) 2

g C)

211

2g D)

211

2g

1l

1l

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30. A wooden block of mass M resting on a rough horizontal surface is pulled with a force F at an angle with the horizontal. If is the coefficient of kinetic friction between the block and the surface, then acceleration of the block is

A) gMF

)sin(cos B) MF /sin

C) cosF D) sinF

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KEY

1. A 2. B 3. C 4. A 5. C 6. B 7. C 8. C 9. A 10. D 11. B 12. C 13. C 14. C 15. C 16. A 17. C 18. B 19. D 20. A 21. A 22. B 23. A 24. B 25. C 26. D 27. C 28. B 29. D 30. A

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SOLUTIONS:

3. Fcos N , N mg Fsin W = F.d. 4.

1/3 mg=2/3 mg

5. 1 2&R R are perpendicular 2netR R 2 cosmg sin 2 cosa g 6. Two blocks remain at rest appF Acts as frictional force for lower block 7. For the block, anet = a - g

212 net

S a t

8. F mg ma

23F mg m a

9. For smooth surface 211 sin2S g t

For rough surface 221 sin cos2S g g t 10. sin cosmg mg Max height = 1 cosR 11.

2 2 sing S

2

sin2S g

13.

sinN P mg cosN P

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14. For 20 Kg 0.6 20 10 20F a For 4 Kg 0.6 20 10 4a 15. 0.2 20 6 2 6 a 4 2N a

6

a

0 20 6 20 20220 6 36

aN N

a

16.

2 220 4f a

f a

2 1 2 4 2020 2f f f

f

3f = 24 F = 8 N 17. direction

F = mg / 2Aa g

/ 4Ba g 34 2 4B A

g g ga

18.

N = 2mg + mg 2cos sin cosN mg

22 cos sin cosmg mg mg

19.

20.

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21 1

2gs

1 0.2 10 12

= 1 m 21.

1sin 2 9.82

mg

22. Friction force = 0.1 9.8 0.98mg N 24. mechE f x f i BCE E f.d

2 BC1 kx mgh mgd2

2

BC

1mgh kx2 0.328

mgd

25.

2k1mgx cos k kx mgx sin2

since i f 0 , k 0

Thus 2

0 0k

(100)(0.200)(2.00)(9.80)(cos37.0 )(0.200) (2.00)(9.80)(sin37.0 )(0.200)2

k 0.115 26.

gvxgxavga 2/2222

27.

weight of overhanging part = lM l1 g

weight of rope lying on the table = glll

M )( 1

gll

lMRRN )(. 1 , glll

MF )( 1

rope will not slide down when Fl

gMl1

1

1 1 1( ) ( )Ml g M l l g or l l l

l l

For maximum value of l1 , 1 1 1( ) 1l l l or l l

28. min, / , /F ma ma mg or a g a g 29.

a = g sin 45 + g cos 45 =

211

221

21

2ggg

30. cos ( sin )F Mg F Ma

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cos sinF Fa gM M

cos sin cos sinF F Fg gM M M