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Topper’s Package Physics - XI Permutation and CombinationsNewton’s Laws of Motion

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1. NEWTONS LAW

1. An air tight cage with a parrot sitting in itis suspended from the spring balance. Theparrot starts flying. The reading of the springbalance will(a) increase (b) decrease(c) no change (d) be zero

2. A force F depends on displacement s as F =5s + 6 and it acts on a mass m = 1 kg whichis initially at rest at a point O. Then thevelocity of the mass when s = 4m is(a) zero (b) 4 2 /m s(c) 8 2 /m s (d) 16 2 /m s

3. A body of mass m has its position x and time

t related by the equation 3/2 13 22

t t . Theinstantaneous force F on the body isproportional to(a) t3/2 (b) t(c) t–1/2 (d) t0

4. A cracker rocket is ejecting 0.05 kg of gasesper second at a velocity of 400 m/sec. Theaccelerating force on the rocket is(a) 20 dyne(b) 20 newton(c) 20 kilogram weight(d) none of these

5. A particle moves in the x-y plane under theinfluence of a force such that its linearmomentum is ˆ ˆ( ) (cos ) (sin )p t A kt i kt j

,

where A and k are constant. The anglebetween the force and the momentum is(a) 0° (b) 30°(c) 45° (d) 90°

6. A machine gun fires a bullet of mass 40 gwith a velocity 1200 m/sec. The man holdingit can exert a maximum force of 144 N onthe gun. How many bullets can be fire persecond at the most ?

(a) Two (b) Four(c) One (d) Three

7. A particle of mass m is acted upon by a force

F given by the empirical law 2F ( )R v tt

. If this

law is to be tested experimentally by observingthe motion starting from rest, the best wayis to plot.

(a) logv(t)against 1t

(b) v(t) against t2

(c) log v(t) against 21t

(d) log v(t) against t

8. The figure shows the position time graph (x– t) graph of one dimensional motion of a bodyof mass 0.4 kg. The magnitude of eachimpulse is

(a) 0.2 Ns (b) 0.4 Ns(c) 0.8 Ns (d) 1.6 Ns

9. A cricket ball of mass 150g has an initialvelocity –1ˆ ˆ(3 4 ) msu i j and a final velocity

–1ˆ ˆ– (3 4 ) msv i j after being hit. Thechange in momentum (final momentum –initial momentum) is (in kgms–1)(a) zero (b) ˆ ˆ(0.45 0.6 )i j(c) ˆ ˆ–(0.9 1.2 )j j (d) ˆ ˆ ˆ–5( )i j i

10. Figures, I, II III and IV depict variation of forcewith time

NEWTON’S LAWSOF MOTION

Unit 3

Topper Package Physics - XI Permutation and CombinationsNewton’s Laws of Motion

31

(I) (II)

(III) (IV)

The impulse is highest in the case ofsituations depicted. Figure(a) I and II (b) III and I(c) III and IV (d) IV only

11. Four particles of mass m, initially at rest, isacted upon by variable force F for a briefinterval of time T. It begins to move with avelocity u after the force stops acting. F isshown in the graphs as a function of time.The curve is a semicircle

F0

F(N)

t(10 s)–3

(a)20

2F

um

(b)

2

8Tum

(c) 04F T

um

(d) 0

2F T

um

12. A rigid ball of m strikes a rigid wall at 60°and gets reflected without loss of speed asshown in figure below. The value of impulseimparted by the wall on the ball will be

(a) 2mV (b) 3

mV

(c) mV (d) 2mV

13. An explosive of mass 9 kg is divided in twoparts. One part of mass 3 kg moves withvelocity of 16 m/s. The kinetic energy of theother part will be(a) 192 J (b) 162 J(c) 150 J (c) 200 J

14. If force on a rocket having exhaust velocityof 300 m/sec is 210 N, then rate ofcombustion of the fuel is(a) 0.7 kg/s (b) 1.4 kg/s(c) 0.07 kg/s (d) 10.7 kg/s

2. IMPULSE AND MOMENTUM CONSERVATION15. A machine gun fires bullets of 50 gm each

at a speed of 1000 m/sec. If an average forceof 200 N is exerted on the gunner, the numberof bullets fired per minute is(a) 240 (b) 120(c) 60 (d) 30

16. The velocity time graph of a body is shownin figure. It implies that at point B

Y

A

V

C

t X

B

(a) the force is zero(b) there is a force towards motion(c) there is a force which opposes motion(d) none of these

17. A player catches a ball of 200 g moving witha speed of 20 m/s. If the time taken tocomplete the catch is 0.5 sec, the forceexerted on the player’s hand is(a) 8N (b) 4N(c) 2N (d) 0N

18. If the kinetic energy of a particle increasesby 300%, the increase in its momentum willbe(a) 20 % (b) 50 %(c) 100 % (d) 200 %

19. Force is applied on an object of mass 2 kg atrest on a frictionless horizontal surface asindicated in the graph. After 1 second thespeed of object in ms–1 is


32

F

t

1.0

20

10

0.5

(a) 7.5 (b) 12.5(c) 15 (d) 25

20. A ball of mass m is thrown vertically upward.What is the rate at which the momentum ofball charges(a) zero(b) mg(c) infinity(d) data is not enough

21. A body of mass 10 kg moves at a constantvelocity of 10 ms–1 Now a constant force actsfor 4s on the body and gives it a speed of2 ms–1 in the opposite direction. The impulseacting on object is(a) 102 Ns (b) –120 Ns(c) 120 Ns (d) 60 Ns

22. A disc of 10g is kept floating horizontally inair by firing bullet, each of mass 5g with thesame velocity at the same rate of 10 bulletper second. The bullet rebound with samespeed in opposite direction. The velocity ofeach bullet at the time of impact is(a) 196 cms–1 (b) 98 cms–1

(c) 49 cms–1 (d) 392 cm–1

23. A particle of mass m moving with velocity umakes an elastic one dimensional collisionwith a stationary particle of mass m. They arein contact for a very brief time T. The forceof interaction increases from zero to F0linearly in time T/2 and decreases linerallyto zero in further time T/2. The magnitudeof F0 is

O

F

T

T/2

F0

time

(a) mu/T (b) 2 mu/T(c) mu/2T (d) none of these

24. A 10 kg wagon is pushed with a force of 7N for 1.5 sec, then with a force of 5 N for 1.7sec and then with a force of 10 N for 3 sec.

What is the change in its velocity(a) 4.9 m/sec (b) 9.8 m/s(c) 10 m/s (d) 9.4 m/s

25. A large number (n) of identical beads, eachof mass m and radius r are strung on a thinsmooth rigid horizontal rod of length L (L >> r) and are at rest at random positions. Therod is mounted between two rigid supports(see figure). If one of the beads is now givena speed v, the average force experienced byeach support after a long time is (assume allcollisions are elastic)

L

(a)

2mvL nr

(b)

2

2mv

L nr

(c)

2

2( )mvL nr (d) zero

26. The adjacent figure is the part of ahorizontally stretched net section AB isstretched with a force of 10 N. The tensionsin the sections BC and BF are

120°

120° 120°

150° 150°

D

C F

E

H

A

GB

(a) 10 N, 11 N(b) 10 N, 6N(c) 10 N, 10 N(d) cannot calcualte due to insufficient data

27. A vessel containing water is given constantacceleration a towards right, along a straighthorizontal path. Which of the followingdiagram represents the surface of the liquid.


33

(a) A (b) B(c) C (d) D

28. A bodyof mass 5 kg starts from the origin withan initial velocity 1ˆ ˆ30 40u i j ms

. If a

constant force ˆ ˆ– ( 5 )F i j N acts on the

body, the time in which the y-component ofthe velocity becomes zero.(a) 5 seconds (b) 20 seconds(c) 40 seconds (d) 80 seconds

29. A body with mass 5 kg is acted upon by a forceˆ ˆ( 3 4 )F i j N . If its initial velocity at t = 0

is 1ˆ ˆ(3 – 12 )v i j ms , the time at which it willjust have a velocity along the Y-axis is(a) Never (b) 5s(c) 2s (d) 16s

30. Two particles of mass m each are tied at theends of a light string of length 2a. The wholesystem is kept on a frictionless horizontalsurface with the string held tight so that eachmass is at a distance ‘a’ from the center P(as shown in figure) Now, the mid-point of thestring is pulled vertically upwards with a smallbut constant force F. As a result, the particlesof move towards each other on the surface.The magnitude of acceleration, when theseparation between them becomes 2x is

m m

a a

P

F

(a) 2 22F am a x

(b) 2 22F xm a x

(c) 2F xm a (d)

2 2

2F a xm a

31. A flat plate moves normally with a speed v1towards a horizontal jet of water of uniformarea of cross-section. The jet dischargeswater at the rate of volume V per second ata speed of v2. The density of water is .Assume that water splashes along the surfaceof the plate at right angles to the originalmotion. The magnitude of the force acting onthe plate due to the jet of water is

(a) Vv1 (b) 1 2( )V v v

(c)21

1 2

V vv v (d)

21 2

2( )V v vv

32. A particle of mass m is at a rest at the originat time t = 0. It is subjected to a force F(t) =F0e–bt in the x-direction. Its speed v(t) isdepicted by which of the following curves

(a) (b)

(c) (d)

33. The tension in the spring is

5N5N(a) zero (b) 2.5 N(c) 5 N (d) 10 N

3. EQUILIBRIUM FORCES

34. A string of negligible mass, going over aclamped pulley of mass m, supports a blockof mass M as shown in the figure. The forceon the pulley by the clamp C is given by

mC

M

(a) 2 Mg (b) 2mg

(c) 2 2( )g M m m (d) 2 2( )g M m M

35. Two blocks of masses 2.9 kg and 1.9 kgare suspended from a rigid support S by twoinextensible wires each of length 1m. Theupper wire has negligible mass and the lowerwire has a uniform mass of 0.2 kg/m. Thewhole system of block, wires and support havean upward acceleration of 0.2 m/s2 (g = 9.8ms/2). The tension at the mid-point of lowerwire is


34

S

A

B

2.9 kg

1.9 kg

(a) 20N (b) 30N(c) 40N (d) 50N

36. A weight W is hung as shown in the figure.Then the tension T is

T

90°

W

(a) sinW (b) cosW (c) cosecW (d) cotW

37. A chain of mass M and length L is heldvertical by fixing its upper end to a rigidsupport. The tension in the chain at adistance y from the rigid support is

(a) Mg (b) ( )Mg L yL

(c)MgLL y (d)

MgyL

38. Two 10 kg. bodies are attached to a springbalance as shown in figure. The reading ofthe balance will be

10 kg 10 kg

Spring scale

(a) 20 kg.-wt. (b) 10 kg.-wt.(c) zero (d) 5 kg.-wt.

39. In the following figure, the pulley is masslessand frictionless. There is no friction betweenthe body and the floor. The accelerationproduced in the body when a force P is appiedto pulling as shown,

P A

(a)PM

(b) 2PM

(c) 3PM (d)

4PM

40. Two weights w1 and w2 are suspended fromthe ends of a light string passing over a smoothfixed pulley. If the pulley is pulled up at anacceleration g, the tension in the string willbe

(a)1 2

1 2

4w ww w (b)

1 2

1 2

2w ww w

(c)1 2

1 2

w ww w

(d)

1 2

1 22w w

w w

41. A block of mass m is at rest under the actionof force F against a wall as shown in figure.Which of the following statement is incorrect?

F

(a) f = mg [where f is the frictional force](b) F = mg [where N is the normal force](c) F will not produce torque(d) N will not produce torque

42. A sphere of mass m is held between twosmooth inclined walls. For sin37 3/5 , thenormal reaction of the wall (2) is equal to(a) mg

37°

37°

12

(b) sin74mg

(c) cos74mg (d) none of these

43. Which of the four arrangements in the figurecorrectly shows the vector addition of twoforces 1F

and 2F

to yield the third force 3F

(a)

1F

2F

3F

(b)

1F

2F

3F

(c)

1F

2F3F

(d)

1F

2F

3F


35

44. Three forces starts acting simultaneously ona particle moving with velocity v

. These

forces are represented in magnitude anddirection by the three sides of a triangle ABC(as shown). The particle will now move withvelocity

A B

C

(a) v

remaining unchanged(b) Less than v

(c) Greater than v

(d) v

in the direction of the largest force BC

45. An object is kept on a smooth inclined planeof 1 in l. The horizontal acceleration to beimparted to the inclined plane so that theobject is stationary relative to the inclined is

(a) 2 1g l (b) 2( 1)g l

(c)2 1

g

l (d) 2 1

gl

46. A block of mass m is placed on a smoothinclined wedge ABC of inclination as shownin the figure. The wedge is given anacceleration a towards the right. The relationbetween a and for the block to remainstationary on wedge is

C B

m

A

a

(a) cosecga

(b) singa

(c) a = g cos (d) a = g tan

4. MOTION OF CONNECTED BODIES

47. A simple pendulum swings in a vertical planeabout the point of suspension O. In theposition shown in the figure, the string hasan angular velocity radian/second. The

instantaneous tension in the string is

(a) cosmg

(b)2

cos lmgg

m

l

O

(c)2

cos lmgg

(d) 2ml

48. As shown in the figure a monkey of certainmass is holding a light rope that passes overa frictionless pulley P. A bunch of bananasB of the same mass is tied to the other endof the rope. In order to get to the bunch,the monkey tries to climb the rope. Thedistance between the monkey and thebananas will

(a) be decreasing

P B

(b) be increasing(c) remain unchanged(d) be uncertain as nothingcan be predicted

49. In the figure, two blocks of 1 20m kg and2 10m kg are in contact with each other

and resting on a frictionless table. A horizontalforce 3F N is applied to mass 1m , thecontact force between 1m and 2m will be?

F

m1 m2

(a) 1N (b) 2N(c) 3N (d) zero

50. With what minimum acceleration can afireman slide down a rope whose breakingstrength is 2/3 of his own weight(a) 2/3 g (b) g(c) 1/3 g (d) zero

51. The elevator in figure is descending with anacceleration of 2 m/s2. The mass of the blockA = 0.5 kg. The force exerted by the block Aon block B is nearly(a) 2N

(b) 4N

2m/s2

B

A (c) 6 N


36

(d) 8 N

52. A frictionless pulley of negligible weight issuspended from a spring balance. Masses of1 kg and 5 kg are tied to the two ends of astring which passes over the pulley. Themasses move due to gravity. During motion,the reading of the spring balance will be

(a) 5/3 kg wt.

(b) 10/3 kg wt.

(c) 6 kg wt.

1kg

5kg (d) 3 kg wt.

53. For the situation shown in figure, with whatforce a 60 kg man pull downward on the ropeto support himself from the floor? (Assumenegligible weight for pulleys and negligiblefriction. (Take g = 10 m/s2)

(a) 600 N

(b) 300 N

(c) 200 N

(d) slightly more than 600 N54. A rope of length L is pulled with a constant

force F. T is the tension in the rope at a point,distance x from the end where the forceis applied. Then, T is

(a)FLx (b) ( )

FLL x

(c)( )F L x

L

(d)( )( )F xL x

55. The pulley and the string shown in figure aresmooth and of negligible mass. For the systemto remain in equilibrium. The angle shouldbe

(a) 0

m m

2m

(b) 30

(c) 45

(d) 60

56. A man slide down a light rope whose breakingstrength is n time his weight (n < 1). Themaximum acceleration of the man so that therope just breaks is(a) g (1 – n) (b) g (1 + n)(c) gn (d) g/n

57. In the arrangement shown. If the surface issmooth the acceleration of the block 2m willbe

(a)2

1 24m g

m m

T m1

T T

m2 (b)

2

1 2

24

m gm m

(c)2

1 2

24

m gm m (d)

1

1 2

2m gm m

58. A pendulum is hanging from the ceiling of acage. If the cage moves upward with aconstant acceleration ‘a’ its tension is T1 andif it is moves down with the same accelerationthe corresponding tension is T2 the tensionin the string, if the cage moves horizontallywith same acceleration a is

T1 T2 T

a

a

a

Ma Mg

(a)2 2

1 22

T T(b)

2 21 2

2T T

(c)2 2

1 22

T T(d)

2 21 2

2T T

59. Two masses of 10 kg and 20 kg are connectedby a massless spring as shown. A force of 200N acts on the 20 kg mass. At a certain instantthe acceleration of 10 kg mass is 12 m/s2.The acceleration of the 20 kg mass at thatinstant is

10 kg 20 kg 200 N

(a) 212 /m s (b) 210 /m s(c) 24 /m s (d) none of these

60. A body of mass m is lying on a wedge of angle


37

as shown in the figure. The accelerationa given to the wedge towards left such thatthe body may fall freely, is

(a) g

(b) tang

m P

R Q

M (c) cotg

(d) sing

61. A simple pendulum is suspended from theceiling of a train which is moving with anacceleration a. The angle of inclination of thependulum from the vertical will be

(a) 90° (b) 0°

(c) 1tan ag

(d) 1tan ga

62. For the same K.E. the momentum shall bemaximum for(a) An electron (b) a proton(c) a neutron (d) an -partical

63. A glass plate can tolerate a maximum weightof 12 kgf. A 10 kg block is placed on the glassplate and this system is moved verticallyupwards with a uniformly increasingacceleration. The glass plate breaks at acertain value of acceleration. The value of thisacceleration is(a) g (b) /2g

(c) /3g (d) /5g

64. A man of mass m = 60 kg is standing onweighing machine fixed on a triangular wedgeof angle = 60° with the horizontal as shown.The wedge is moving up with an upwardacceleration of a = 2 m/s2. The weightregistered by machine is

(a) 600 N

(b) 1440 N

a

(c) 360 N

(d) 240 N65. The block B moves to the right with a

constant velocity 0v as shown in the figure.The relative velocity of body A with respectto body B is (assuming all pulleys and stringsare ideal )

mm

v0

(a) 012

v towards left

(b) 012

v towards right

(c) 032

v towards right

(d) 032

v towards left

66. System shown in figure is in equilibrium andat rest. The spring and string are massless,now the string is cut. The acceleration ofmass 2m and m just after the string is cutwill be

(a) /2g upwards, g downwards

(b) g upwards, /2g downwards2m

m(c) g upwards, 2g downwards

(d) 2g upwards, g downwards

67. Assuming all the surfaces to be frictionless,acceleration of the block C shown in thefigures is

(a) 25 /m s

(b) 27 /m sA B

3 m/s2 4 m/s

2

Ca(c) 23.5 /m s

(d) 24 /m s

68. All surfaces shown in figure are smooth.System is released with the springunstretched. In equilibrium, compression inthe spring will be

m

45°

M


38

(a) 2mg

k (b)2mg

k

(c)( )

2M m g

k

(d)mgk

69. A lift of total mass M is raised by cables fromrest to rest through a height h. The greatesttension which the cables can safely bear isnMg. The maximum speed of lift during itsjourney if the ascent is to made in shortesttime is

(a)12 ngh

n

(b) 2gh n

(c) 21

nghn

(d)12 ngh

n

5. FRICTION

70. A is a 100 kg block and B is a 200 kg block.As shown in fig. the block A is attached toa string tied to a wall. The coefficient offriction between A and B is 0.2 and thecoefficient of friction between B and floor is0.3. Then the minimum force required tomove the block B will be (take 210 /g m s )(a) 600 N

(b) 800 N

F A B (c) 900 N

(d) 1100 N

71. Assuming the coefficient of friction betweenthe road and tyres of a car to be 0.5, the max.speed with which the car can move arounda curve of 40 m radius without slipping, onan unbanked road, is(a) 25 m/s (b) 19 m/s(c) 14 m/s (d) 11 m/s

72. A block is lying on an inclined plane whichmakes 60° with the horizontal. If thecoefficient of friction between block and theplane is 0.25 and g = 10 m/s2, thenacceleration of the block when it moves alongthe plane will be(a) 22.50 /m s (b) 25.00 /m s(c) 27.41 /m s (d) 28.66 /m s

73. A block of mass m lying on a rough horizontalplane is acted upon by a horizontal force P and

another force Q inclined at an angle tothe vertical. The block will remain inequilibrium if the coefficient of frictionbetween it and the surface is

P

Q

(a)sincos

P Qmg Q

(b)

cossin

P Qmg Q

(c)cossin

P Qmg Q

(d)

sincos

P Qmg Q

74. A block of mass 4 kg rest on an inclined plane.The inclination of the plane is graduallyincreased. It is found that when theinclination is 3 in 5. The block just beganto slide to the down. The coefficient of frictionbetween the block and the plane is

5

4

3

(a) 0.4 (b) 0.6(c) 0.8 (d) 0.75

75. A block of weight w is held against a verticalwall by applying a horizontal force of 75 N. Thesurface of the wall is rough. Now

(a) 75 > w

(b) 75 = w 75N R

W

y

(c) 75 < w

(d) can not be prediceted

76. An insect crawl up a hemispherical surfacevery slowly. The coefficient of friction betweenthe insect and surface is 1/3. If the linejoining the centre of the hemisphericalsurface to the insect makes on angle withthe vertical. The maximum possible value of is given by(a) cot 3

(b) tan 3

Mg

(c) sec 3

(d) cosec 3


39

77. A slab of 40 kg is lying on a frictionless floorand a block of 10 kg rests on the slab as shownin the figure. The coefficients of static andkinetic friction between the slab and theblock are 0.6 and 0.4 respectively. If a forceof 100 N is applied on the block, then the netacceleration of the slab will be

10kg

40 kg

100 N

Frictionless Floor

(a) 210.0 /m s (b) 25 /m s(c) 20 /m s (d) 21 /m s

78. A block of mass 1 kg is at rest on ahorizontal surface in a truck. The coefficientof static friction between the block and surfaceis 0.6. If the acceleration of the truck is

25 /m s , then the friction force acting on thisblock is(a) 2 N (b) 3 N(c) 5 N (d) 6 N.

79. A smooth block is released at rest on a 45°incline and then slides a distance d. The timetaken to slide is n times as much to slide onrough incline than on a smooth incline. Thecoefficient of friction is

(a) 211sµ

n (b) 2

11sµn

(c) 211kµ

n (d) 2

11kµn

80. The upper half of an inclined plane withinclination is perfectly smooth while thelower helf is rough. A body starting from restat the top will again come to rest at the bottomif the coefficient of friction for lower half isgiven by(a) tan (b) 2tan

(c) 2cos (d) 2sin

81. M

m F

Smooth surface

µ is the coefficient of static friction between

the two blocks. Maximum value of F for whichthe two blocks move together without anyrelative displacement, is(a) µmg (b) ( )µ M m g

(c) ( )mµ M m gM

(d) ( )Mmµ M m gm

82. In the figure, 2Am kg and 4Bm kg . Forwhat minimum value of F, A starts slippingover B ( 210 /g m s )

B

A

F

µ =0.21

µ =0.42

(a) 24N (b) 36N(c) 12N (d) 20N

83. The system is pushed by a force F as shownin figure. All surfaces are smooth exceptbetween B and C. Friction coefficient betweenB and C is µ. Minimum value of F to preventblock B from downward slipping is

2m 2mmFA B C

(a)32

mgµ

(b)52

mgµ

(c)52

µmg

(d)32

µmg

84. Three blocks A, B and C of equal mass m areplaced one over the other on a smoothhorizontal ground as shown in figure.Coefficient of friction between any two blocksof A, B and C is 1/2. The maximum valueof mass of block D so that the blocks A, B andC move without slipping over each other is

A

B

C

D

(a) 6 m (b) 5 m(c) 3 m (d) 4 m


40

85. A block A of mass m is placed over a plankB of mass 2 m . Plank B is placed over asmooth horizontal surface. The coefficient offriction between A and B is 1/2. Block A isgiven a velocity 0v towards right. Accelerationof B relative to A is

A

B

v0

(a) /2g (b) g(c) 3 /4g (d) zero

86. In the given figure the wedge is fixed pulleyis frictionless and string is light. Surface ABis frictionless whereas AC is rough. If theblock of mass 3m slides down with constantvelocity, then the coefficient of frictionbetween surface AC and the block is

(a) 1/3

(b) 2/33mm

A

B45° 45°

C(c) 1/2

(d) 4/3

87. A block of mass 4 kg is kept over a roughhorizontal surface. The coefficient of frictionbetween the block and the surface is 0.1. At

ˆ0, 3 /t m s i velocity is imparted to the blockand simultaneously ˆ2 ( )N i force starts actingon it. Its displacement in first 5s is(a) 8 i (b) 8 i(c) 3 i (d) 3 i

88. Two bodies of mass m and 4m are attachedwith string as shown in the figure. The bodyof mass m hanging from a string of length lis executing oscillations of angular amplitude

0 while the other body is at rest. Theminimum coefficient of friction between themass 4m and the horizontal surface shouldbe

0

4m

m

(a)02 cos

3

(b)2 02cos

2

(c)01 cos

2

(d)03 2cos

4

89. A block A is placed over a long rough plankB of same mass as shown in figure. The plankis placed over a smooth horizontal surface. Attime 0t , block A is given a velocity 0v inhorizontal direction. Let 1v and 2v be thevelocities of A and B at time t. Then choosethe correct graph between 1v or 2v and t :

B

v0A

(a)t

v1

v2

orv1 v2

(b)t

v1

v2

orv1 v2

(c)t

v1v2

orv1 v2

(d)t

v1v2

orv1 v2

90. A parabolic bowl with its bottom at origin hasthe shape 2 /20y x . Here x and y are inmetres. The maximum height at which asmall mass m can be placed on the bowlwithout slipping (coefficient of static frictionis 0.5) is(a) 2.5 m (b) 1.25 m(c) 1.0 m (d) 4.0 m

91. A rocket is fired vertically from the earth withan acceleration of 2g, where g is thegravitational acceleration. On an inclinedplane inside the rocket, making an angle with the horizontal, a point object of massm is kept. The minimum coefficient offr ict ion min between the mass and theinclined surface such that the mass does notmove is(a) tan2 (b) tan(c) 3 tan (d) 2 tan

92. Given in the figure are two blocks A and Bof weight 20 N and 100 N, respectively. Theseare being pressed against a wall by a forceF as shown. If the coefficient of frictionbetween the blocks is 0.1 and between blockB and the wall is 0.15, the frictional forceapplied by the wall on block B is


41

F BA

(a) 120 N (b) 150 N(c) 100 N (d) 80 N

93. A uniform chain of mass M and length L islying on a table in such a manner that a partof it is hanging down from the edge of the tableas shown. If the coefficient of friction is µ,then the maximum length of the chain thatcan hang without sliding is

(a)Lµ (b) 1

Lµ

(c) 1µL

µ (d) 1µL

µ 94. A rod AB rests with the end A on rough

horizontal ground and the end B against asmooth vertical wall. The rod is uniform andof weight W. If the rod is in equilibrium inthe position shown in the figure, the normalreaction at point B is

Ax

y

B

30°

(a) zero (b)32W

(c) W (d) 3W

95. A circular disc with a groove among itsdiamter is placed horizontally. A block of mass1 kg is placed as shown. The co-efficient offriction between the block and all surfaces ofgroove in contact is = 2/5. The disc has an

acceleration of 25 m/s2. Find the accelerationof the block with respect to disc

a = 25 m/s2

cos = 4/5 sin = 3/5

(a) 10 m/s2 (b) 5 m/s2

(c) 20 m/s2 (d) 1 m/s2

96. Two blocks, 4 kg and 2 kg are sliding downan incline plane as shown in figure. Theacceleration of 2 kg is

4kg2kg

=0.3

=0.2

30°

(a) 1.66 m/s2 (b) 2.66 m/s2

(c) 3.66 m/s2 (d) 4.66 m/s2

97. A car is negotiating a curved road of radiusR. The road is banked at an angle . Thecoefficient of friction between the tyres of carand the road is s. The maximum safe velocityon this road is

(a)2 ( tan )

1 tans

sgR

(b)

( tan )1 tan

s

sgR

(c)( tan )1 tan

s

s

gR

(d) 2

( tan )1 tan

s

s

gR

98. A block of mass m1 rests on a horizontal table.A right light string connected to it passes overa frictionless pulley at the edge of table andfrom its other end another block B of massm2 suspended. The coefficient of kineticfriction between the block and the table is k.When the block A is sliding on the table, thetension in the string is

(a)2 1

1 2

( )( )

m kmgm m

(b)

1 2

1 2

(1 )( )

km m gm m

(c)1 2

1 2

(1 )( )

km m gm m

(d)

2 1

1 2

( )( )

km mgm m


42

6. INTEGER ANSWER TYPE99. Consider the following arrangement of two

blocks A and B. Coefficient of friction betweenthe two blocks A and B is 0.3. There is nofriction between the block B and ground. Pulleysand string are light. Find the maximum valueof F (in N) for which there is no slipping betweenthe two blocks (mA = 1 kg and mB = 3 kg).

A

F

Smooth

B

µ=0.3

100. The system shown in equilibrium. When springis cut, then what will be the initialacceleration of lower block?

3kg

2kg

k = 20 N/m

101. A body of mass 4 kg is moving at speed 2 m/son circular path of radius 1 m speed of particleis continuously increasing at rate of 3 m/s2.Force acting on particle at the instant whenspeed 2 m/s is 5n N. Find the value of n.

102. Two blocks of 4 kg and 6 kg are attached bysprings, they are hanging in vertical position,lower spring breaks due to excessive force.Acceleration of 4 kg block just after breakingis 5n m/s2. Find the value of n.

4kg

k = 200 N/m

k = 100 N/m

6kg

103. Consider the arrangement shown in the figure.The mass m2 is 12 kg. Friction coefficientbetween m2 and ground is 0.25. All other contactsurfaces are frictionless. Find the maximumvalue of m1 (in kg) for which the systemremains in equilibrium.

m1

m2

53oµ = 0

µ = 0.25

104. A block is moving on an inclined plane makingan angle 45° with the horizontal and thecoefficient of friction is µ. The force required tojust push it up the inclined plane is 3 timesthe force required to just prevent it from slidingdown. If we define N = 10 µ, then N is __ .

105. A block of mass m = 2 kg is resting on a roughinclined plane of inclination 30° as shown infigure. The coefficient of friction between theblock and the plane is µ = 0.5. What minimumforce F (in newton) should be appliedperpendicular to the plane on the block, so thatthe block does not slip on the plane ?

30°

F

106. A block A of mass m is placed over a plank B ofmass 2 m. Plank B is placed over a smoothhorizontal surface. The coefficient of frictionbetween A and B is 0.4. Block A is given avelocity v0 towards right. Find acceleration (inms–2) of B relative to A.

v0A

B


43

1. NEWTONS LAW1. a 2. c 3. c 4. b 5. d6. d 7. a 8. c 9. c 10. c11. c 12. c 13. a 14. a

2. IMPULSE AND MOMENTUM CONSERVATION15. a 16. c 17. a 18. c 19. a20. b 21. b 22. b 23. b 24. a25. b 26. c 27. c 28. c 29. b30. b 31. d 32. c 33. c

3. EQUILIBRIUM OF FORCES34. d 35. a 36. c 37. b 38. b39. b 40. a 41. b 42. a 43. c44. a 45. c 46. d

4. MOTION OF CONNECTED BODIES47. b 48. c 49. a 50. c 51. b52. b 53. c 54. c 55. c 56. a57. a 58. c 59. c 60. c 61. c62. d 63. d 64. c 65. c 66. a67. c 68. d 69. d

5. FRICTION70. d 71. c 72. c 73. a 74. d75. b 76. a 77. d 78. c 79. d80. b 81. c 82. b 83. b 84. c85. c 86. c 87. d 88. d 89. b90. b 91. b 92. a 93. d 94. b95. a 96. b 97. b 98. b

6. INTEGER TYPE QUESTION99. (4) 100. (0) 101. (4) 102. (3) 103. (6)104. (5) 105. (8) 106. (6)

Topper’s Package Physics - XI Permutation and ......2020/07/15 · Topper’s Package Physics -...

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