Motion Question Bank for IIT JEE

7/29/2019 Motion Question Bank for IIT JEE

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QUESTION BANK

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Match the column type questions

1. For a particle moving along a circle of radius r, at a given instant of time

ListI ListII

I) Centripetal acceleration = 0 implies that A) ac = 0

II) Tangential acceleration = 0, implies that B) aT = 0

III) If speed is increasing C) angle between velocity and

a is obtuse

IV) If the speed is decreasing D) angle between

Ca and

a is acute

A) I-A, II-B, III-D, IV-CD B) I-A, II-C, III-D, IV-B

C) I-B, II-C, III-A, IV-D D) I-D, II-A, III-B, IV-C

2. A particle is performing circular motion. Then if

ListI ListII

I) It has a constant speed, then A) It cant follow a circular path

II) It has a varying speed, then B) It can have varying magnitude of acceleration

III) It has varying velocity, then C) It has constant magnitude of acceleration

directed towards the centre.

IV) It has a constant velocity, then D)Its acceleration also has a tangential component

A) I-A, II-D, III-C, IV-A B) I-A, II-B, III-D, IV-A

C) I-D, II-C, III-A, IV-B D) I-D, II-A, III-B, IV-C

3. Two particles A and B are moving in 2concentric circles of radii rA and rB respectively in same plane. The

angular velocity of A is A and that of B is B . At t = 0, both are in same phase, then if

ListI ListII

I) BA and 2rA = rB =r, then relative A) 2/5

angular velocity of B w.r.t. A at t = 0, is

II) BA

2 and rA = 2rB =r, then relative B) 2/


III) BA 3 and 3rA = rB =r, then relative C) zero


IV) 2/BA and rA = (rB/3 )=r, then relative D) 2/


A) I-B, II-D, III-C, IV-A B) I-A, II-B, III-C, IV-D


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C) I-C, II-A, III-B, IV-D D) I-A, II-D, III-C, IV-B

4. A particle is moving along a parabolic path y = x2. At the instant when the particle is at (1, 1).

ListI ListII

I) ac of the particle tasm2

/22 of the particle = 1 m/s2,

then acceleration of particle in ,r coordinate is A) ^^

10

97

10

173

r

II) ac and22

/1/22 smaandsma tc then acceleration

of particle in (x-y) coordinate is B) ^^

5

6

10

1

52

423

r

III)22

/7/3 smaandsma tc , then acceleration of

particle in ,r coordinate is C) ^^

5

241

215

2

ij

IV)22

/7/3 smaandsma tc , then acceleration of

particle in (xy) coordinate is D) ^^

5

67

5

372ij

A) I-B, II-C, III-A, IV-D B) I-A, II-B, III-C, IV-D


5. A particle is following a path x2 = y(2y) (x, y > 0) and y(t) =t2. Now at t = 1s.

ListI ListII

I) x coordinate of the particle is A) 6

II) magnitude of ac of the particle is B) 1

III) radius of curvature is C) 5

IV) speed of the particle is D) 5 / 6

A) I-A, II-B, III-C, IV-D B) I-B, II-A, III-D, IV-C


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6. A particle is moving in circle in x-y plane of equation x2 + y2 = 1 with an angular velocity '' , if

ListI ListII

I) 0,cotcos 00 VVVy and the particle

covers complete circle in 2/ sec, then A) at2

1,

2

1 yx

II) 0,cotcos 00 VVVy , and '' is 8 rad/sec, then B) at time xVsec,8/ will beV0

III) 0,2/sin 00 VtVVy and 2t

at t sec,4/t then C) at time xVsec,16/ will beV0

IV) 0,4/cos 00 VtVVy , if sec/4rad D) at xVyx ,21

,2

1

will be

2/0V

A) I-A, II-D, III-C, IV-B B) I-A, II-B, III-C, IV-D

C) I-C, II-A, III-B, IV-D D) I-B, II-C, III-B, IV-AD

7. A particle is performing circular motion such that 0 . The acvs tand tsv / graphs for the motion are

plotted in left column

ListI ListII

I) A) aT < 0

II) B) aT = 0


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III) C) particle is speeding up

IV) D) particle is speeding down

8. A particle is moving along a circle x2 + y2 = a2 in horizontal plane with angular velocity =

2rad/sec. A man is moving along the x = 2a in + direction with velocity 4a m/s in the same plane. At t = 0,particle and man are along line y = -a

ListI ListII

I) At 2/t , the angle made by the line of motion of

particle with line parallel to x-axis w.r.t. man is A) 221tan 1 II) At 8/t the angle made by the line of motion of

particle with line parallel to x-axis w.r.t. man is B) aji

^^

422

III) At 4/3t , the velocity of particle w.r.t. man is C) 2/

IV) At , the angle made by the line of motion of particle

with the line parallel to x-axis w.r.t. man is D)^^

42 jaia

A) I-A, II-B, III-C, IV-D B) I-B, II-C, III-A, IV-A


9. A particle moving in horizontal plane along a curve whose equation in polar coordinates is cos2ar

ListI ListII

I) If ,60&/5/0 sraddtd then A) 2/21

3

100sm

aaN

II) If V = 10a m/s and ,300 then B) 2/

3

50sm

aaT

III) If 02

2

453

25

and

dt

d, then C)

2/100 smaaN


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IV) If ,2/sec/10 radandrad then D) 2/32

50sm

AaT

E) 2/0 smaT

A) I-A, II-B, III-C, IV-D B) I-CD, II-BC, III-AB, IV-CE


10. A massless ring is rolling on frictionless surface with velocity V and angular velocity '' such that V =

ListI ListII

I) Acceleration vectors of points A & B are A) Directed towards centre

II) Velocity vectors of points A & B are B) perpendicular to each other.

III) Acceleration vectors of points B & C are C) at angle 450 with each other.

IV) Velocity vectors of points B & C are D) in opposite directions

A) I-C, II-C, III-C, IV-A B) I-A, II-B, III-C, IV-D

C) I-AB, II-C, III-AD, IV-B D) I-A, II-D, III-C, IV-B

Kinematics-I

11. A drunkard man moves 5m east 10m north and then 20m southwest. Find out the total distance and

displacement traced.

12. A wheel is rolling on horizontal surface. Find out the displacement of a point mark at the bottom most point on

wheel of radius R which rolls half revolution.

13. In the above example consider the point on the extreme right. Get the disp. for half revolution.


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14. In a circular motion, plot the graph of displacement vs angle .

15. A train moves a distance s with speed v1 and comes back along same path same distance s with speed v2. Find

out average speed and average velocity.

16. If the train moves with speed v1 for first half time and speed v2 for second half-time. Find out the average

displacement.

17. A particle has initial velocity = 10m/s east, acceleration = 5m/s2 is given in north direction. Find out the final

velocity and displacement at t = 2 sec and direction.

18. A train starts form rest with acceleration = a, moves uniformly and then retards with retardation b, then comes

to rest. If total displacement travelled is s, find the minimum time taken to cover the distance.

19. A balloon starts rising up with an acceleration a = 5m/s2, at t = 4 sec. the stone is de-attached, which first rises

up and then comes down. Find out the total time taken of stone before hitting the ground. Plot the displacement

vs. time graph.

20. Consider the disp. X as a function of time t. x = 4tt2

21. Consider the potition x as a function of t. x = (t -1)(t -2)(t-3)

22. The particle A is moving with constant velocity u and B approaches A with a velocity v, initial separation

being l.


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23. A man of height 1.5m moves away from a bulb 6m high with speed 2m/s. Find out velocity of shadow.

24. A stone is dropped form the top of a t tower of a unknown height h. At the instant it has fallen c metres, a

second stone is released from rest from a point b m below the top of tower (b > c). The two stones strike the

ground at the same time. Determine the height of tower.

25. A stone is dropped in air at height 39m above ground, due to wind blowing it has horizontal acc. ax =

1.2m/s2. Describe its path and find out range.

26. Two cars are moving with velocities v1 and v2 towards the crossing (v1 > v2). Taking their initial separation

from crossing being a each. Find out the relative velocity of car B w.r.t. A and min. separation between them.

27. A motor boat going downstream overcame a raft at point A. After one hour it turned back and met the raft

again at a distance 6km from point A. Find the river velocity.

28. Two boys at the bank of river started swimming simultaneously with same speed w.r.t water, one swims

perpendicular to the stream and other aims to do so. Other boy deflected by some distance from the destination

now he walks to the destination. If both reach the destination at the same time, find out speed of walking of

other boy. (Take velocity of flow = 3, velocity of each boy in still water = 5 km/hr)


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29. A balloon starts rising from the earths surface. The accession rate is constant and equal to v0. Due to the wind,

the balloon gathers the horizontal velocity component vx = ky where k is a constant any is a height of ascent.

Find how the following quantities depend on the height of ascent.

a) The horizontal drift of the balloon x(y).

b) The total tangential and normal accelerations of the balloon.

30. Two trains initially separated by distance L are heading towards each other on same track each with speed v,

and a bird flies form train A towards B with constant speed w > v reaches train B and immediately comes back

to A with same speed and continues to do so till it sandwiches between the two. Find out the number of trips

and time taken before it sandwiches. Show the situation graphically.

31. A car is moving with constant velocity 25m/s ahead 100m of a jeep starts accelerating a = 2m/s2. Show that the

two values of time the car and jeep are at the same position and show the situation graphically.

MCQS with one correct answer

32. A particle moves according to eq. t = ax2 +bx, find the retardation at any instant.

a) 32

2

baxa

b) 2a c) 22

2

baxa

d) None of these

33. A particle falls from a height h. In the last 0.2sec it travels 6m. Find the height h.

a) 48.05m b) 420.05m c) 32.05m d) None of these

34. A particle starts with an acc. from rest for sometime and after achieving max. velocity starts retarding at rate

and finally comes to rest. If total time taken t, its max. velocity during the motion will be

a)

t

b) t

2

c) t

2

d) t

2

2

35. A water tap leaks such that water drops fall at regular intervals. Tap is fixed 5cm above the ground. First drop

reaches the ground when 4th

is about to leave the tap. Find the separation between 2nd

and 3rd

drop.

a) m3

2b) m

3

4c) m

3

5d) None of these


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36. An elevator is descending with uniform acc. To measure the acc. a person in the elevator drops a coin

6ft.above the floor of the elevator. The coin strikes the floor in 1sec. Find the acc. of elevator.

a) 20 ft/s2 b) 10 ft/s2 c) 16 ft/s2 d) None of these

37. A police jeep is chasing with velocity 45km/h. A thief in another jeep is moving with 155km/h. Police fires a

bullet with a muzzle velocity 180m/s. The bullet strikes the jeep of the thief with a velocity

a) 27 m/s b) 150 m/s c) 250 m/s d) 450 m/s

38. A truck is moving with a velocity 36km/h. On seeing red light it decelerates at 2m/s. The reflex time of the

driver is 0.4sec. How much distance will truck travel before coming to a stop?

a) 25 m b) 29 m c) 35 m d) None of these

39. A clock has minute hand of 10cm length. The average velocity of the tip of minute hand form 6am to 6:30am

is

a) 2 / 3 cm/min b) 3/2 cm/min c) 3/ cm/min d) None of these

40. A river is 1km wide and flows at a rate 4km/h. A man is capable to swim 3kw/h. Where will he land if he

strikes normally to the flow of river?

a) 1km just opposite bam b) km3

4away c) km

4

3away d) None of these

41. Rain falling vertically downwards with a velocity of 3km/h. A person moves on a straight line road with a

velocity of 4km/h. Then the apparent velocity of the rain w.r.t. the person is

a) 1 km/h b) 5 km/h c) 4 km/h d) 3 km/h

Objective questions with more than one correct choices

42. Two cars A and B start from rest and move together for the same time interval. Their acceleration graphs are as

follows:

a) Both the cars attain the same velocity after 10sec.


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b) The velocity of car B is more than that of A after 10sec.

c) The distance travelled by the car B is more than that of A after 10sec.

d) Both the cars travel the same distance after 10 sec.

43. A particle moves 10m in the first 2sec, 20m in the next 3sec and 30m in the next to 10sec. Which of the

following statement(s) is (are) true for this motion?

a) The particle was uniformly accelerated

b) The particle had decelerating forces acting on it part of the motion

c) The average speed of the particle was 4 m/s.

d) The average acceleration of the particle was 3 m/s 2

Comprehension Questions : I

For spiral motion, the angular displacement as well as the radius keep on changing w.r.t. time, if the radius is

defined as a function of angular disp. fr , it changes w.r.t. . Hence the particle will have tangential

and radial component in polar coordinates.

Radial velocitydt

dr

t

PM

t

OPOM

00limlim Tangential velocity

dt

dr

t

r

t

QM

sinlimlim

00

44. A particle moves along a path defined by polar coordinates r = 2et and2

8t rad, its tangential velocity at t =

1 sec is

a) 87 m/s. b) 174 m/s c) 43 m/s d) 54 m/s

45. Its radial velocity at t = 1sec is

a) 8.7 m/s b) 87 m/s c) 5.4 m/s d) 54 m/s

Directions. Q: 36 38: In mathematic, the symbol [.] is used for greatest integer which the max. possible value in

integer for that real number e.g., [4.3] = 4 and [-6.3] = -7. Consider a function of acc. as time a = [t-1], if the

body starts from rest t = 0

46. Find out the velocity at t = 3sec.

a) 3 m/s b) 2 m/s c) 1 m/s d) 0 m/s

47. Find out the disp. at t = 3 sec


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a) 4 m b) 2 m c) 0 m d) -2 m

48. During the motion the body has reversed its direction of motion at

a) t = 1sec. b) t = 2 sec c) t = 3 sec d) t = 1.5 sec

Match the following:

49. ListI ListII

I) Tangential acc. is zero A) Rectilinear uniform motion

II) Only normal acc. is zero B) Uniform circular motion

III) Resultant acc. is zero C) Non-uniform circular motion.

IV) None of the acc. is zero D) Uniformly accelerated moiton.

a) I-B, II-D, III-C, IV-A b) I-B, II-D, III-A, IV-C

c) I-D, II-C, III-A, IV-B d) I-A, II-B, III-C, IV-D

50. Consider the following graphs, where a = acc., v = vel., s = disp.

ListI ListII

I) A) Possible

II) B) Possible

III) C) Impossible

IV) D) Impossible

a) I-C, II-B, III-A, IV-D b) I-B, II-C, III-D, IV-A

c) I-C, II-D, III-B, IV-A d) I-A, II-D, III-B, IV-C


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Numerical Questions

51. Two steel balls fall freely on an elastic slab. The first ball is dropped from a height h1 and the second from a

height h2(h2 < h1), T sec after the first ball. After the passage of time T, the velocities of the balls coincide in

magnitude and direction. Determine the time T and the time interval during which the velocities of the two

balls will be equal assuming that the two balls do not collide.

NEWTONS LAWS OF MOTTION

52. The mass of each ball is m. radius r. and diameter of the cylindrical container is 7r/2. Find out the normal

contact force between the two balls

53. Three identical cylinder are place symmetrical on conjugate inclined plane as shown. Find out the min. value

of angle for this to be in equilibrium.

54. A heavy rope of mass M, length L is resting on a smooth horizontal surface, it is being pulled by force F. Find

out tension on it at a distance x from the free end.

55. Two blocks of mass 1kg and 2kg are connected by a rubber cord, 2kg block is being pulled with force 10N. If

acc. of this block is 2m/s2, find out acc. of other block at that moment.

56. Find out the force exerted by man to keep himself balanced, and normal reaction force between man and plank.


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57. Check the balance of beam.

58. Find out the free F applied by support and angle for equilibrium.

59. If a spring (k) is cut into two parts of length ratio n : 1, find out the spring constant of each part

60. A smooth semicircular wire track of radius R is fixed in a vertical plane. One end of a massless spring of

natural length 3R/4 is attached to the lowest point O of the wire track. A small ring of mass m which can slide

on the track is attached to the other end of spring makes an angle 600

with the vertical. The spring constant, k =

mg/R. Consider the instant when the ring is released.

a) Draw F.B.D of ring b) Find out tangential acc. of ring and normal reaction on it


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61. Find out acc. of blocks and force exerted by clamp. (Take, m = 1kg)

62. There is a groove cut on the surface of inclined plane, as shown. Find out the time taken by a block released at

top to travel length, L of groove.

63. Find out the height h of inclined plane if a block placed at top takes minimum time to slide down. Base length

b is constant.

64. Two particles each of mass m are connected by a light string of length 2L as shown. A continuous force F is

applied at the midpoint of the spring (x = 0) at right angles to the initial position of the string. Show that acc. of

m in the direction at right angle to F given by222 xL

x

m

Fax

.

65. Suppose a lift accelerating up with acceleration = a. Find out the acc. of each block w.r.t. lift and tension in the

string.


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MCQs with one correct answer

66. A uniform chain of length L and mass m lies on a smooth horizontal table with its length perpendicular to the

edge of the table and small part overhanging. The chain starts sliding down from rest due to the weight of

hanging part. Find the acceleration and velocity of the chain when length of the hanging portion is x.

a)L

xg

L

xg2

, b) xgL

xg, c) gL

L

xg, d) xLg

L

xg,

67. If is coefficient of friction between the tyres and road, then the minimum stopping distance for a car of mass

m moving with velocity v is

a) gv b)g

v

2

2

c) g2

d)g

v

2

68. Aballoon of mass M is under a drag force F and upthurst T. It is moving down with a uniform velocity v. What

amount of mass be removed so that it starts rising up with same velocity v?

a) MT/g b) 2T / g c) T / g d) 2(M-T/g)

69. Consider the shown arrangement. Assume all surfaces to be smooth. If N represents magnitudes of normal

reaction between block and wedge, then acceleration of M along horizontal equals

a)M

N sinalong +ve x-axis b)

M

N cosalong +ve x-axis

c)M

N sinalong -ve x-axis d)

Mm

N

sinalong -ve x-axis

70. In the above problem normal reaction between ground and wedge will have magnitude equal to

a) mgN cos b) mgMgN cos c) MgN cos d) mgMgN sin

71. A pendulum of mass hangs from a support fixed to a trolley. The direction of the string when the trolley rolls

up a plane of inclination with acceleration, a, is


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a) zero b) tan-1 c)

cos

sintan

1

g

gad) tan-1

g

a

72. Two masses m and M are attached with strings as shown. For the system to be in equilibrium, we have

a)m

M21tan b)

M

m21tan c)

m

M

21tan d)

m

M21tan

73. All surfaces shown in the figure are smooth. System is released with the spring unstretched. In equilibrium,

compression in the spring will be

a)k

mg

2

b)k

mg2c)

k

gmM

2

d)

k

mg

74. A sphere of mass m is held between two smooth inclined walls. For sin370 = 3/5, the normal reaction of the

wall (2) is equal to

a) mg b) mg sin 740 c) mg cos 740 d) None of these


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Objective Questions wit more than one correct choice

75. A uniform rope of mass m hangs freely form a ceiling. A monkey of mass M climbs up the rope with an

acceleration a. The force exerted by the rope on the celling is

a) Ma + mg b) M(a + g) + mg

c) M(a + g) d) dependent on the position of monkey on the rope

76. The system shown in the figure is released from rest. The spring gets elongated, y

a) M > m b) M > 2m c) M > m/2

d) For any value of M (Neglect friction and masses of pulley, string and spring).

77. In the figure s > d. Masses m1 and m2 are connected by a light inextensible string passing over a smooth pulley.

When the system is released, then mass m1 will acceleration towards the pulley provided.

a) 32

1 m

mb) 3

2

1 m

mc)

2

3

2

1 m

md) None of these

78. At the instant t = 0 a force F = kt (k is constant acts on a small body of mass m resting on a smooth horizontal

plane. The time when body leaves the surface, is

a)k

mg sinb)

mg

k sinc)

sink

mgd) sinkmg

79. Certain force gives mass m1 an acceleration a1 and mass m2 and acceleration a2. Then the acceleration the force

would give to an object of mass M will be


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a)21

21

21 , mmMifaa

aa

b)

12

21

21 , mmMifaa

aa

c) 2121 , mmMifaa d)2

1

2

1 ,m

mMif

a

a

80. The acceleration of blocks of mass 5 kg and 10kg are

a) zero, if F = 100 N b) a1=5 m/s2

and a2 = 0, if F = 300N

c) a1 = 15 m/s2, a2 = 2.5m/s

2, if F = 500N d) Acceleration of the masses are independent of F

81. Five identical cubes each of mass m are on a straight line two adjacent faces in contact on a horizontal surfaces

as shown in fig. Suppose the surface is frictionless and a constant force P is applied from left to right to the end

face of A; which of the following statement are correct?

a) The acceleration of the system is 5 P/m

b) The resultant force acting on each cube is P/S

c) The force exerted by C and D is 2P/5

d) The acceleration of the cube D is P/Sm

Match Type Questions

82. Match the acc. of block m in each ease.

ListI ListII

I) A) a = g


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II) B) g

III) C) g / 3

IV) D) a = 0

a) I-A, II-B, III-C, IV-D b) I-A, II-C, III-B, IV-A

c) I-B, II-C, III-D, IV-A d) I-D, II-B, III-A, IV-C

Comprehension Questions Passage -1:

Two pulleys are arranged as shown in fig. (pulleys are massless and frectionless). P 1 is beingpulled up by a time varying force F.

83. The velocity of 5kg block the moment 1kg is lifted up is

a) zero b) 225 m/s c) 750 m/s d) 1500 m/s

84. The velocity of 1kg block the moment 5kg is lifted up, is

a) zero b) 225 m/s c) 750 m/s d) 1500 m/s

85. The height gained by 1kg block at t = 30 sec is


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a) 2250 m b) m4

15000c) m

12

17000d) zero

86. The height gained by 5kg block at t = 30sec is

a) 2250 m b) m4

15000c) m

12

17000d) zero

87. If the string attached to surface can sustain max. force up to 35 N, then max. time the system will sustain is

a) 70 sec. b) 140 sec. c) 700 sec. d) 35 sec.

Numerical Problems

88. Fig. shows a block of mass m attached to a spring of force constant k and connected to ground by two strings

making an angle 900

with each other. In relaxed state natural length is l. In the situation shown in fig. find the

tension in the two strings.

89. Fig. shows a block A on a smooth surface attached with a spring of force constant k to the ceiling. In this state

spring is in natural length l. The block A is connected by a massless and friction less string to another identical

mass B hanging over a light and smooth pulley. Find the distance moved by A before it leaves contact with the

ground.

Assertion & Reason Type Questions

Directions. Q: 82-86 : The following questions consist of two statements. One labeled as Assertion and other as

Reason. Consider these statements and answer.

a) If both Assertion and Reason are true and Reason is correct explanation of Assertion


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b) If both Assertion and Reason are true but Reason is not correct explanation of Assertion

c) If Assertion is true but Reason is false. d) If both Assertion and Reason are false

90. Assertion: Forces of action and reaction do not cancel each other. Each produces its own effects

Reason: Forces of action and reaction are equal and opposite.

a) b) c) d)

91. Assertion: A body under the influence of concurrent forces in equilibrium either remains at rest

or moves with a constant velocity.

Reason: Concurrent forces are said to be in equilibrium when the magnitude of the resultant

force is zero.

a) b) c) d)

92. Assertion: A block of mass M is suspended by a light cord C and a stronger cord D is attached

to the lower end. A sudden jerk is given to D, then block remains at its place.

Reason : Tension in chord C is less than that in D

a) b) c) d)

93. Assertion: Two bodies of mass 50g and 20g are allowed to fall from the same height. If air resistance for each

is same, then both the bodies reach the earth simultaneously.

Reason : Acceleration of both the bodies is same.

a) b) c) d)

94. Assertion: A bird is sitting on the floor of a wire cage and the cage is in the hand of a boy. Even when the bird

starts flying in the cage, the boy does not experience any change in the weight of the cage

Reason : Bird is still in the cage because of which the boy does not experience any change.

a) b) c) d)

NEWTONS LAWS

95. In each of the following arrangements, find (a) acceleration of the system of blocks

(b) tension in each string


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(i) ii) iii)

iv) v) vi)

vii) viii) ix)

96. In each of the arrangements given, find the acceleration of each particle just after the force/s shown in the

figure applied. All the particles were initially at rest. You may leave the answer in terms of x and y

components. Neglect gravity if not mentioned specifically. Assume that the block does not leave the table.

a) b) c) d)

e) f) g) h)


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97. In each of the following arrangements, find the acceleration of each block and tension in the thread/s just after

the blocks are released from rest. Consider gravity

a) b)

98. Two small particles are restricted to move along the edges of a smooth wire cube as shown in the figure. They

are also connected by an ideal thread. If the mass of each particle is M, find the acceleration of each particle

just after the system is released from rest. One of the system is released from rest. One of the sides containing

particle is horizontal and other is vertical.

99. In each of the following cases, some particles are moving along a rope as shown in the figures. Find the tension

in all the sections of the rope in each case. Neglect gravity in parts a, e, f. All acceleration are given w.r.t the

thread.

a) b) c) d)

e) f)

100. In the following thread/pulley systems, calculate the acceleration of each mass and tension in each thread.

Assume that all the threads and pullies are ideal and that the systems are released from rest.


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24

a) b) c) d)

e) f)

g) h)

i) j)

101. In each of the following cases, find the net force applied by the threads on each of the clamps.

a) b) c)


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ROTATIONAL MOTION (Single option correct)

102. Find moment of inertial of a semicircular disc of mass m and radius R about an axis passing through point P

about an axis passing through point P (see Fig.) of semi circle and perpendicular to plane of the disc

a)4

2MRb)

2

24

MRc)

4

2

32MR d)

4

3

22MR

103. A force of magnitude 20 unit acts along the vector 2i3j + 4k at point i + j + 2k. Find magnitude of torque

about y-axis.

a)29

560b)

29

3100c)

20

529d)

20

329

104. A triangle ABC where AB = 3, BC = 4, CA = 5 units and G is the centroid to triangle. The minimum and

maximum moment of inertia will be about line

a) AG, CG b) CG, BG c) BG, AG d) BG, CG

105. For a body making rotation according to2

15 BtAt . If the angular momentum vector reverts its

direction twice at an interval of sec2t , and the torque is zero at t = 4sec, then the values of A and B are

a) 1, 8 b) 8, 1 c) 4, 1 d) 1, 4

106. A rod of uniform mass of length L can freely rotate in a vertical plane about an axis passing through O. The

angular velocity of the rod when it falls from position P to P through an angle is

a) sin5

6

L

gb)

2sin

6

L

gc)

2cos

6

L

gd) sin

6

L

g


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107. A light thin hoop of radius R is attached with six point mass equal to m each according to fig., moving without

slipping on the track. Find the angular momentum of mass B about the point of contact P of the hoop when the

mass A at the point P, take speed of D equal to 2v.

a)2

3mvrb)

2

mvrc) mvr d)

3

2mvr

108. Two point masses of mass m and speed v stick to an equilateral triangle made by three massless rods at the end

B and C. The system is placed at smooth plane and masses stick simultaneously moving normal to sides. The

angular velocity after the collision will be

a)2

3vb)

3

2vc)

3

vd) v2

109. A light cylinder placed on a surface with coefficient friction 5.0 is attached with a thin rod of mass m is

released from rest as shown in Fig. Find the acceleration of centre of rod after the release

a)2

gb) g c) 0 d) g2

110. A sphere of mass M and radius r (see Fig.) slips on a rough horizontal plane. At some instant it has

translational velocity v0 and rotational velocity about the centre v0 /2r. The translational velocity after the

sphere starts pure rolling, is


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a) 6v0/ 7 in forwards direction b) 6v0/ 7 in backwards direction

c) 7v0/ 7 in forwards direction d) 7v0/ 6 in backwards direction

111. A particle of mass m = 5kg is moving with a uniform speed of smv /23 in xy plane along the line y = (x

+ 4). The magnitude of the angular momentum (in kg. m2/sec) about origin is:

a) zero b) 60 c) 7.5 d) 240

112. A ring of mass 0.3kg and radius 0.1m and a solid cylinder of mass 0.4kg and of the same radius are released

simultaneously on a flat horizontal surface such that they begin to roll with the same KE as soon as released

towards a wall which is at the distance from the ring and the cylinder. Then

a) the cylinder will reach the wall first b) the ring will reach the will first

c) Both will reach the wall simultaneously d) None of these

113. A thin uniform L shape rod of mass 4kg is hinged as shown. When the thread is cut find the initial acceleration

of point A.

a)22

3gb)

5

23gc)

2

3gd)

3

2g

More than one options may be correct

114. A thin rod of length 6m & mass 6m is given a sharp impulse of 120 N-sec at point 2m from an end according

to fig. The rod is placed on a smooth horizontal plane. Just during impulse rod breaks up in two parts at the

point of impulse. Assuming impulse to be divided equally in both parts the relative angular velocity of parts

will be


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a)

sec

30rad

b)

sec

150rad

c)

sec

120rad

d) None of these

115. Two similar particles A and B rotate in xy plane of radius rA and yz plane of radius rB around vertical axis

passing through the centre of their orbits. The uniform angular velocity of A is A and that of B is B , then

relative angular acceleration and angular velocity are

a) AB b)22

2

1,

4BA

AB

c) 22 BA d)22

2 BABA

116. Two persons of equal mass m are sliding freely on ice, each with a speed v on parallel straight path in opposite

directions. The paths are separated by a perpendicular distance d. the first person carries a pole of length lheld

firmly at one end. The second person grips the other end of the pole just as they are passing each other. Which

of the following statements are true for the subsequent motion in a circular path?

a) Each person moves in a circular path of radius l2

1with constant speed v.

b) Each persons moves in a circular path of radius2

labout a centre which itself moves with

speed v.

c) The tension in the pole remains constant

d) They come to rest when the pole has rotated through2

to lie along the direction of original

motion.

117. The torque on a body about a given point is found to be equal to A x L where A is a constant vector and L is

angular momentum of the body about that point from this. It follows that

a)td

ldis perpendicular to L at all instant of time.


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29

b) The component of L in the direction of A does not change with time.

c) The magnitude of L does not change with time

d) L does not change with time

118. A ball rolls down an inclined plane and acquires a velocity vr, when it reaches the bottom of the plane. If the

same ball slides without friction on other plane and acquires rolling from the same height down an equally

inclined smooth plane and acquires a velocity vs, which of the following statements is/are correct?

a) vr< vs because a work is done by the rolling ball against the frictional force.

b) vr> vs because the angular velocity acquired makes the rolling ball to travel faster.

c) vr= vs because kinetic energy of two balls is same at bottom of plane.

d) vr< vs, because the rolling ball acquires rotational as well as translational kinetic energy.

119. Two similar thin rods of mass m each making an angle of 1200 are hinged at point P (see Fig.) when a F = 6mg

is applied to hinge at angle of 1200 form both rods. (Neglect the effect of gravity). For t = 0sec. select the

correct options.

a) Linear acceleration of centre of rods will be 3g each.

b) Acceleration of point A will be 3g

c) Acceleration of point A will be more than 3g

d) Linear acceleration of centre of rods will be less than 3g

120. A uniform disc of radius 1m is first allowed to spin about its axis with angular velocity of 4 rad/s and then

carefully placed with its flat face on a horizontal surface. The coefficient of friction is 3/1 . Take g =

10m/s2. Then

a) the angular retardation produced will be (40/9) rad/s2

b) the angular retardation produced will be (10/3) rad/s2

c) the disc will stop rotating after t = 0.9 sec

d) the disc will stop rotating after t = 2 sec

121. A ring rolls without slipping on a horizontal surface. At any instant, its position is as shown in the fig. Then


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a) section ABC has greater kinetic energy than section ADC.

b) section BC has greater energy than section CD

c) section BC has the same kinetic energy as section DA.

d) the section AB, BC, CD and DA have the same kinetic energy

Comprehension -A

Force of friction plays a role of turning force in motion of a rolling rigid body. The force of friction always

tries to oppose the relative motion between the two surfaces in contact. As a force it can produce linear

acceleration as well

122. A solid sphere rotating with an angular speed is put on a long plank of mass equal to sphere. The friction

exists between plank and sphere while plank rests on a plane frictionless surface, then

a) speed of centre of sphere will increase first then decrease.

b) speed of centre of sphere will increase then become constant.

c) the plank will have same acceleration as sphere will have.

d) speed of centre of mass of the system will be half of that of speed of centre of sphere.

123. Choose the correct options(s)

a) Total kinetic energy will increase

b) Total kinetic energy will decrease

c) Translational kinetic energy of the system will increase

d) Total energy will be remain same

124. Choose the correct options (s)

a) The angular momentum of sphere and plank will not conserve.

b) The angular momentum will conserve only about the centre of sphere.

c) The angular momentum will conserve about all points.

d) Angular momentum of the system will conserve only about the point of contact where force

of friction acts


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31

From stational K.E. of the plank will be equal to

a) b) c) d)

Comprehension -B

A solid cylinder of radius R and mass M rolls over an inclined plane with inclination 045 with its axis

horizontal. Let the friction coefficient between the plane and cylinder be and length of plane to travel be L

= 20m. Then if cylinder starts with rest, what will be the parameters of motion? (take g = 10m/sec2)

125. Choose the correct option(s)

a) If were greater than 1/3 the motion would be pure rolling

b) If is less than 1/3 there will be loss of kinetic energy during motion

c) If 0 or 3/1 , there will be no loss of mechanical energy

d) There will always be a loss of mechanical energy whatever be the value of

126. If =1/6, relative velocity of point of contact at time t, is

a)3

220 tb) t

22

10c) t

3

30d)

3

25t

127. Mechanical energy loss will be maximum for the value of equals to

a)3

1

b)4

1

c)6

1

d) 12

1

128. Loss of mechanical energy in above case in S.I. units is

a) 210m b) 2100m c)2

100md)

2

10m

Comprehension -C

Turning effect of a force is given by torque, where Fr . A force may produce turning as well as linear

effect. Consider a solid sphere of mass m and radius r in space where there is no gravity or any other force, a

force F is applied tangentially to the sphere by some mean the direction of force does not change by time.


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129. The solid sphere will move in a

a) straight line b) circular path c) toroide path d) parabolic path

130. The solid sphere will have

a) linear accelerate only b) angular acceleration only c) will have both d) None of these

131. Choose the correct option

a) Linear accelerationm

F b) Angular acceleration

mr

F

2

5

c) Both of these d) No angular acceleration

132. The sphere will have kinetic energy in time

a)m

tF

2

22

b)m

tF 22

8

7c)

m

tF 22

4

7d)

m

tF

4

22

Subjective Questions

133. A thin uniform rod AB of mass m = 1.0kg moves translationally with acceleration2

/0.2 sm due to two

antiparallel force F1 and F2 (fig.). The distance between the points at which these forces are applied is equal to

a = 20cm. Besides, it is known that F2 = 5.0 N. Find the length of the rod.

134. A sphere, a disc and a ring of the same mass and radius are rolled from rest from the top of a frictionless

inclined plane simultaneously. In which order do they reach the bottom of the incline?

135. A uniform ladder of mass 20kg and length 4m rests against a smooth wall where friction coefficient with

ground be 5.0 . If g = 10m/sec2, what maximum angle ladder could make with vertical measure angle in

degrees?


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136. A uniform rod of mass 5.0kg and length l= 90cm, rests on a smooth horizontal surface, one of the end of the

rod is struck with the impulse J = 3.0 N-s in horizontal direction perpendicular to the rod. As a result, the rod

obtains the momentum p = 3.0 N-s. Find the K.E. with which rod will move.

Matching Type Questions

137. ListI ListII

For a body rolling down on a inclined Here t1 < t2 < t3 < t4 mass and radius are

plane with out slipping, the time taken same for all bodies

to reach bottom will be

I) Ring A) t3

II) Solid sphere B) t2

III) Solid cylinder C) t4

IV) Hollow sphere D) t1

a) I-D, II-C, III-B, IV-D b) I-C, II-D, III-B, IV-A

c) I-D, II-B, III-D, IV-C d) I-D, II-B, III-A, IV-C

138. ListI ListII

I) Torque A) r x p

II) Angular Momentum B)

2

L

III) Power C) r x F

IV) Energy D)

a) I-C, II-A, III-B, IV-D b) I-A, II-C, III-D, IV-B

c) I-C, II-A, III-D, IV-B d) I-A, II-C, III-B, IV-D

139. ListI ListII

I) A) MI will be mr2

3

II) B) 22

2

14

RRM


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III) C) 22

2

1 54

RRM

IV) D) 22

2

12

RRM

a) I-B, II-D, III-C, IV-A b) I-B, II-C, III-D, IV-A

c) I-D, II-A, III-B, IV-C d) I-C, II-B, III-D, IV-A

140. ListI ListII

I) Torque angular acceleration, angular A) Tensor

momentum, angular velocity

II) Momentum of inertia B) Radial vectors

III) Angular displacement of finite value,

rotational kinetic energy C) Axial vector

IV) Centripetal acceleration, centripetal force D) Not vectors

a) I-C, II-A, III-D, IV-B b) I-B, II-D, III-A, IV-C

c) I-A, II-C, III-B, IV-D d) I-B, II-A, III-D, IV-C

141. A block of mass 0.1kg is held against a wall by applying a horizontal force of 5N on the block. If

the coefficient of friction between the block and wall is 0.5, the magnitude of frictional force

acting on the block is

a) 2.5 N b) 0.98 N c) 4.9 N d) 0.49 N

142. A block of mass 2kg rests on a plane inclined at an angle of 300 with the horizontal. The

coefficient of friction between the block and surface is 0.7. What is the frictional force acting on

the block?

a) 11.9 N b) b) 9.82 N c) 15.75 N d) 5.8 N


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143. A 5kg stationary bomb is exploded in three parts having mass 1 : 1 : 3 respectively. Parts

having same mass move in perpendicular direction with velocity 39 m/s, then the velocity of

bigger part is

a) sm /2

13b) sm /210 c) sm /

2

10d) sm /213

144. A ship of mass 3 x 107kg initially at rest is pulled by a force of 5 x 10

4N through a distance of

3m. Assuming that the resistance due to water is negligible, what will be the speed of ship?

a) 0.1 m/s b) 1.5 m/s c) 5 m/s d) 0.2 m/s

145. Two masses of 10kg and 20kg respectively are tied together by a massless spring. A force of 200N is applied

on a 20kg mass. At the instant shown, the acceleration of 10kg mass is 12m/s2, the acceleration of 20kg mass is

a) 0 m/s b) 10 m/s2

c) 4 m/s2

d) 12 m/s2

146. A board of mass 5kg is suspended from a horizontal beam by two supporting wires, each at an angle of 450 to

the vertical. The tension of each wire is (g = 10ms2)

a) 50 N b) 35 N c) 12.5 N d) 20 N

147. A given object takes n times more time to slide down a 450 rough inclined plane as it takes to slide down a

perfectly smooth 450

incline. The coefficient of kinetic friction between the object and incline is

a)2

1

1

nb)

2

11

n c)

2

11

n d)

21

1

n

148. In a rocket, fuel burns at the rate of 1kg/s. This fuel is ejected form the rocket with a velocity of 60km/s. This

exerts a force on the rocket equal to

a) 60 N b) 600 N c) 6000 N d) 60000 N


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149. A block B of mass M = 15kg hangs by a cord from a knot K of mass mkwhich hangs from a ceiling by means

of two other cords. The cords have negligible mass, and the magnitude othe gravitational force of the knot is

negligible compared to the gravitational force. The tensions in the three cords are

a) NTNTNT 104,134,147 321 b) NTNTNT 147,134,104 321

c) NTNTNT 147,104,134 321 d) NTNTT 147,134,,0 321

150. There are two force on the 2.0kg box. Only one force is shown. The figure also shows the acceleration of thebox. The magnitude of second force along with direction is

a) 38 N, 2130 b) 20 N, 2130 c) 42 N, 1800 d) 58 N, 1800

151. An 11kg salami is supported by accord that runs to a spring scale, which is supported by another cord form the

ceiling (Fig.1). The spring scale gives reading in weight units. Now the salami is supported by a cord that runs

around a pulley and to a scale (as shown in Fig.). In third case the wall has been replaced by a second 11kg

salami on left, and assembly is stationary. The reading of the scale in the three cases is [ g = 10m/s2]

a) 11 kg, 22kg, 44kg b) 110kg, 220kg, 440kg c) 11kg, 44kg, 55kg d) Same in all three cases


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152. When a nucleus captures a stray neutron, it must bring the neutron to a stop within the diameter of the nucleus

by means of the strong force. That force which glues the nucleus together is approximately zero outside the

nucleus. Suppose that a stray nucleus with an initial speed of 1.4 x 107 m/s is just barely captured by a nucleus

with diameter d = 1.0 x 10-14m. Assuming that the strong force on the neutron is constant, the magnitude of this

force is

[Given neutrons mass is 1.67 x 10-27kg]

a) 4 N b) 16 N c) 8 N d) 32 N

153. A 40kg girl and an 8.4kg sled are on the frictionaless ice of a frozen lake, 15m apart but connected by a rope of

negligible mass. The girl exerts a horizontal 5.2N force on the rope. Then how far from the girls initial

position do they meet?

a) 1.3 m b) 6.2 m c) 2.6 m d) Data Insufficient

154. A sphere of mass 3.0 x 10-4kg is suspended form a cord. A steady horizontal breeze pushes the sphere so that

the cord makes a constant angle of 370

with the vertical. The tension in the cord is given by

a) 3.7 x 10-3 N b) 2.2 x 10-3 N c) 6.8 x 10-3 N d) 8.5 x 10-3 N

155. Two blocks are in contact on a frictionaless table as shown. A horizontal force (F = 3.2N) is applied to the

larger block. A force of same magnitude is applied to the block of smaller mass but in opposite direction. The

force between the blocks in first case is 21 fandf in second case. Also given m1 = 2.3kg, m2 = 1.2kg. Then,

which one of the following holds true?

a) 21 ff b) 21 ff c) 21 ff d)2

2

1

ff

156. A 5.00kg block is pulled along a horizontal frictionless floor by a cord that exerts a force of magnitude F =

12.0 N at an angle0

25 above the horizontal. The magnitude of blocks acceleration just before it is lifted

(completely) off the floor is


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a) 2.18 m/s2

b) 21 m/s2

c) 5.18 m/s2

d) 11 m/s2

157. A chain consisting of five links, each of m = 0.100kg is lifted vertically with a constant acceleration of 2.50

m/s2. The magnitude of the force on link 3 form link 4 is

a) 2.46 N b) 0.25 N c) 3.69 N d) 4.92 N

158. If a cars wheels are locked (kept from rolling) during emergency braking, the car slides along the road.

Ripped-off bits of tire and small melted sections of road form the skid marks that reveal that cold welding

occurred during the slide. The skid mark was 290m long. Assuming that cars acceleration is constant during

the braking and 60.0 , how fast was the car going when the wheels become locked?

a) 90 km/hr b) 210 km/hr c) 80 km/hr d) 120 km/hr

159. A man pulls a loaded sled of mass m = 75kg along a horizontal surface at constant velocity. The coefficient of

kinetic friction k between the runners and the snow is 0.10 and angle is 420. What is the magnitude of the

forcea

T on the sled from the rope?

a) 91 N b) 41 N c) 22 N d) 0 N

160. A coin of mass m is at rest on a book that has been tilted at an angle with the horizontal. When is

increased to 130, the coin is on the verge of sliding down the book, which means that even a slight increase

beyond 130 producing sliding. The coefficient of static friction between the coin and book is


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a) 0.5 b) 0.33 c) 0.19 d) 0.23

161. A 1.34kg sphere is connected by means of two massless strings, to a vertical, rotating rod. The strings are tied

to the rod and are taut. The tension in the upper string is 35 N. The tension in the lower string is

a) 8.74 N b) 6.45 N c) 9.98 N d) 7.48 N

162. A 1000 kg boat is traveling at 90 km/hr when its engine is shut off. The magnitude of the frictional force

a

kf

between boat and water is proportional to the speed of the boat. vfk 70 where v is in meters per second

and kf in Newtons. The time required by the boat to slow to 45 km/hr is

a) 1 s b) 5 s c) 12.8 s d) 9.9 s

163. The mass of an elevator (lift) is 500 kg. The tension in the cable elevator when the elevator is ascending with

an acceleration of 2ms-2 is

a) 5900 N b) 4900 N c) 3900 N d) 2900 N

164. The masses M1, M2, M3 of three bodies are 5, 2 and 3 kg. The values of tensions T 1, T2 and T3 will be how

much, when the whole system is going upward with an acceleration of 2ms-2?

a) T1 = 29.4 N, T2 = 98 N, T3 = 98 N b) T1 = 98 N, T2 = 49 N, T3 = 29.4 N

c) T1 = 35.4 N, T2 = 118 N, T3 = 59 N d) T1 = 118.4 N, T2 = 59 N, T3 = 35.4 N


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40

165. A small cart with a sphere suspended over it by a string approaches an inclined plane at a speed v. In which

direction, with respect to the vertical will the string supporting the sphere be deflected when the cart begins to

climb the cart begins to climb the inclined plane?

a) will remain vertical. b) will be perpendicular to the inclined plane.

c) will be horizontal. d) none of these

166. A block A of mass 7kg placed on a frictionless table. A thread tied to it passes over a frictionless pulley and

carries a body B of mass 3kg at the other end. The acceleration of the system is (g = 10 ms2)

a) 30 m/s2 b) 3 m/s2 3) 10 m/s2 4) 1 m/s2

167. A particle starts moving in a straight line with constant acceleration a. At a time t1 second after the beginning

of motion, the acceleration changes sign, remaining the same in magnitude. Determine the time from the

begining of motion, till it returns to the starting point.

a) 221 t b) 21t c)2

1t

d) 221 t

168. A person walks up a stationary escalator in 90 seconds. If the escalator moves with person, first standing on it,

it will take 1 minute to reach the top from ground. How much time would it take him to walk up the moving

escalator?

a) 3 s b) 12 s c) 36 s d) 48 s

169. A block slides down a rough inclined plane of slope angle with constant velocity. It is then projected up the

same plane with an initial speed v0. How far up the plane will it move before coming to rest?


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41

a)sin

2

0

g

vb)

sin4

2

0

g

vc)

2

singd)

sin

22

0

g

v

170. A block of mass m slides in an inclined right-angled trough as shown. If the coefficient of kinetic friction

between block and material composing the trough is k , find the acceleration of block.

a) cos2sin kg b) cos2sin kg

c) sincos kg d) cossin2 kg

171. An aeroplane of mass 10,000 kg requires a speed of 20ms-1, for take off the run on the ground being 100m. The

coefficient of kinetic friction between the wheels of the plane and ground is 0.3. Assume that plane accelerates

uniformly during take off. The minimum force required by the engine to take off

a) 2 x 104N b) 5 x 104N c) 3 x 104N d) 4 x 104N

172. A caterpillar crawls up a fixed hemispherical bowl of radius R. If the coefficient of friction is3

1. Find the

height as percentage of radius upto which caterpillar can crawl.

a) 3% of R b) 5% of R c) 7% of R d) 9% of R

ROTATIONAL DYNAMICS-II (Practice Sheet-3)

173. In each of the following mass/pulley systems, mass of each pulley is m and radius is r. All threads are massless

and there is sufficient friction between threads and pullies to prevent slipping between them. There is no

friction between any other surface. Treat each pulley as a uniform disk. In each case, find the acceleration of

each mass after the system is released form rest.


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42

a) b) c)

d) e)

174. Figure shows two blocks of masses m and M connected by a string passing over a pulley. The horizontal table

over which the mass m slides is smooth. The pulley has a radius r and moment of inertia I about its axis and it

can freely rotate about this axis. Find the acceleration of the mass M assuming that the string does not slip on

the pulley

175. A string is wrapped on a wheel of moment of inertia 0.20kg-m2 and radius 10cm and goes through a light

pulley to support a block of mass 2.0kg as shown in the figure. Find the acceleration of the block.

176. The pulley shown in the figure has a radius 10cm and moment of inertia 0.5kg-m2

about its axis. Assuming the

inclined planes to be frictionless and fixed, calculate the acceleration of the 4.0kg block.


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43

177. Solve the previous problem if the friction coefficient between the 2.0kg block and the plane below it is 0.5 and

the plane below the 4.0kg block is frictionless.

178. A light rod of length 1m is pivoted at its centre and two masses of 5kg and 2kg are hung from the ends as

shown in the figure. Find the initial angular acceleration of the rod assuming that it was horizontal in the

beginning.

179. Suppose the rod in the previous problem has a mass of 1kg distributed uniformly over its length. (a) Find the

initial angular acceleration of the rod. (b) Find the tension in the supports to the blocks of mass 2kg and 5kg.

180. In each of the following cases, some block/s is/are attached to a step pulley. In each case, taking moment of

inertia of the step pulley to be I, find its angular acceleration. All pullies except step pullies are massless and

frictionless.

a) b) c)

181. Two objects are attached to ropes attached to wheels on a common axle as shown in the figure. The total

moment of inertia of the two wheels is 40kg-m2. The radii are R1 = 1.2m and R2 = 0.4m.


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a) If m1 = 24 kg, find m2 such that the system is in equilibrium

b) If 12 kg is gently added to the top of m1, find the angular acceleration of the wheels and the tension in the

ropes.

ROTATIONAL DYNAMICS-II (Practice Sheet-4)

182. In each of the following cases, a body is rotating about a given axis with uniform angular speed . Find the

reaction force applied by axis of rotation on the body at the instant line joining points A and B is parallel to x-

axis. Neglect gravity and friction.

a) b)

c) d)

183. Each of the given arrangements shows a body that is free to rotate about a horizontal axis. The body is initially

held at rest and released from the position shown in the figure. In each case, just after the release, find

i) angular acceleration of the body.

ii) acceleration of centre of mass of the body


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iii) force being applied on the body by the axis of rotation

a) b) c) d)

184. A rod AB of length L and mass m is lying horizontally on a horizontal frictionless table. The rod is pivoted

about the end A. Suppose that a horizontal force of magnitude F is applied on end B, such that is always

perpendicular to the length of the rod. Just after the force is applied, find:

a) angular acceleration of the rod. b) angular speed of the rod

c) acceleration of centre of mass of the rod. d) force being applied by the rod on the pivot

e) force of interaction between a small particle of mass dm at the midpoint of the rod and rest ofthe rod. f) force applied by one half of the rod on the other.

185. Three particles A, B and C, each of mass m, are connected to each other by three massless rigid rods to from a

rigid, equilateral triangular body of side l. This body is placed on a horizontal frictionless table (x-y plane) and

is hinged to it at the point A so that it can move without friction about the vertical axis through A (see fig.).

The body is set into rotational motion on the table about A with a constant angular velocity .

a) Find the magnitude of the horizontal force exerted by the hinge on the body

b) At time T; when the side BC is parallel to the x-axis, a force F is applied on B along BC

(as shown). Obtain the x-component and the y-component of the force exerted by the hinge

on the body, immediately after time T.

186. A uniform rod AB of mass m = 2kg and length l= 100cm is placed on a sharp support O such that AO = a =

40cm and OB = b = 60cm. A spring of force constant K = 600 Nm -1 is attached to end B as shown in the

figure. To keep the rod horizontal, its end A is tied with a thread such that the spring is elongated by y = 1cm.

Calculate reaction of support O on the rod when the thread is burnt (g = 10 ms-2).


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187. Frame ABC shown in the figure is rotating with constant angular velocity in a gravity freee region. At the

instant shown in the figure, find the force applied by part AB of frame on part BC. Express your answer in

terms of

^

i and^

j .

ROTATIONAL DYNAMICSI (Practice Sheet -1)

188. In each of the following cases, calculate the magnitude of net torque acting on the body about the given axis of

rotation. Symbol (-) denotes that the axis of rotation is perpendicular to the plane of paper and symbol

denotes that the axis of rotation is in the plane of paper.

a) b) c) d)

e) f) g) f)


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i) j) k)

k) m) n)

o)

189. Determine the magnitude of net torque acting on the body shown in each case about the given axis of rotation.

a) b) c)


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d) e) f)

g) h) i)

190. Determine the moment of following forces about the specified points. Express your answer in unit vectors

^

i ,

^

j ,^

k . Also specify the axis of rotation in each case.

a)

^^

2 jiF

acting at (4, 6) about (0, 0). b)

^^

2kiF

acting at (4, 6) about (0, 0).

191. Consider a force

^^

64 ji acting on a large sphere centred at origin. Force is acting at the point (0, 0, 2).

If the sphere can rotate about origin, find the equation of axis of rotation.

ROTATIONAL DYNAMICSI (Practice Sheet -1)

192. Consider a light rod with two heavy mass particles at its ends. Let AB be a line perpendicular to the rod as

shown in the figure. What is the moment of inertia of the system about AB?

193. Three particles, each of mass 200g, are kept at the corners of an equilateral triangle of side 10cm. Find the

moment of inertia of the system about an axis

a) joining two of the particles; and

b) passing through one of the particles and perpendicular to the plane of the particles.


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194. Particles of masses 1g, 2g, 3g,100g are kept at the marks 1cm, 2cm, 3cm,.100 cm respectively on a metre

scale. Find the moment of inertia of the system of particles about a perpendicular bisector of the metre scale.

195. The moment of inertia of a uniform rod of mass 0.50kg and length 1m is 0.10kg-m2 about a line perpendicular

to the rod. Find the distance of the from the middle point of the rod.

196. Two uniform identical rods each of mass m and length lare joined to from a cross as shown in the figure. Find

the moment of inertia of the cross about a bisector as shown by the dotted line dotted in the figure.

197. Three rods each of mass m and length lare joined together to from an equilateral triangle as shown in the

figure. Find the moment of inertia of the system about an axis passing through its centre of mass and

perpendicular to the plane of the triangle.

198. A rod of length lis pivoted about an end. Find the moment of inertia of the rod about this axis if the linear

mass density of rod varies as mkgbax /2 .

199. A thin wire is bent to from a circular ring of radius R. The linear density of the wire varies as ke0 ,

20 , 0 and kare constants and is the an angle shown in the figure. Find the moment of inertia

of the ring about an axis passing through is centre and perpendicular to is plane.


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200. A thin uniform wire is bent to from a spiral whose equation is given by:

20,0 kerr . Find

the moment of inertia of the spiral piece of wire about z-axis (see figure).

201. Find the moment of inertia of the rod AB about an axis y as shown in the figure. Mass of the rod is m and

length is l.

202. A thin steel wire is bent into the shape shown. Denoting the mass per unit length of the wire by m, determine

by direct integration the moment of inertia of the wire with respect to each of the coordinate axes. (symmetry

in x, y).

203. A flat rectangular plate has variable superficial density given by x0 , where 0 is a constant and x is

the distance measured along x-axis. (see figure). Find the moment of inertia of the plate about (i) y-axis

(ii) x-axis (iii) z-axis


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204. Determine the moment of inertia of an ellipse of semi axes a and b, about (i) the major axis, and (ii) the minor

axis. Use the perpendicular axis theorem to determine the moment of inertia of the ellipse about an axis

perpendicular to the plane of the ellipse through the centre.

205. Determine the moment of inertia of a laminar circular sector of radius R and mass M, making an angle of 600

at the centre, about an axis passing through the centre of the outermost rim x and perpendicular to the plane of

the sector.

206. The mass of circular disc in m. A circular hole is now cut into it as shown in the figure. Find the moment of

inertia of the remaining part about an axis passing through point A perpendicular to the discs plane.

207. The surface density (mass/area) of a circular disc of radius a depends on the distance from the centre as

BrAr . Find its moment of inertia about the line perpendicular to the plane of the disc through itscentre.

208. A flat semicircular disc of radius R has variable surface density given by y0 where 0 is a constant

and y is the distance measured along y-axis. Find the moment of inertia of the plate about:

i) xaxis ii) y-axis iii) z-axis


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209. A flat circular disc of radius R has variable density given by 2

0 sin where 0 is a constant and

is the angle made with x-axis. Find the moment of inertia of the disc about an axis passing through its

centre, perpendicular to its plane.

210. The solid cylinder has an outer radius R, height h, and is made form a material having a density that varies

from its centre as2ark , where k and a are constants. Determine the mass of the cylinder and its

moment of inertia about the z-axis.

211. Find the moment of inertia of a truncated cone about its axis, the radii of its ends being a and b.

212. The paraboloid is formed by revolving the shaded area around the x-axis. Determine the radius of gyration kx.

The material has a constant density .

213. The area shown is revolved about the x-axis to from a homogeneous solid of revolution of mass m. Using

direct integration, express the moment of inertia of the solid with respect to the x-axis in terms of m and h.

214. Find the moment of inertia of a hollow sphere about a diameter, its external and internal radii being a and b.

215. Determine the moment of inertia of the homogeneous triangular prism with respect to the y-axis. Express the

result in terms of the mass m of the prism.


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Friction in Rotational Mechanics

216. Find out the minimum friction coefficient so that the cylinder does not slip on inclined plane

217. A ladder is resting over the rough wall and rough surface. Find out the angle for equilibrium.

218. Find out min. friction coefficient to topple this hexagon on rough surface

219. Find out force F required to maintain the plank over two rollers.


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220. Find out the max. angle for equilibrium of hemisphere resting at the corner of a room, take friction

coefficient for each surface.

221. A disc of mass M and radius R is in pure rolling by the application of force F at height h. Decide how the

friction force changes its direction w.r.t. height of force application.

222. Discuss the minimum friction coefficient for objects (i) Ring (ii) Disc (ii) Solid sphere (iv) Spherical shell

rolling on inclined plane about bottom most point

223. Find out the minimum friction coefficient to prevent slipping

224. Find out the maximum value of T for pure rolling of spool. Spool may be considered as disc of radius R and

mass M.


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225. Find out the acceleration of plank and cylinder and their friction forces for pure rolling

226. A solid sphere and a thin spherical hoop of equal mass m and radius R are harnessed together by rigging and

free to roll without slipping down the inclined plane as shown. Neglecting the mass of rigging, determine the

force in rigging. Assume frictionless bearing.

227. A rope is wrapped over the rough pulley ad tries to rotate pulley. Friction coefficient between them is and

the angle made by rope at centre is . Find out how T1 is related to T2.

228. Consider a solid sphere and cube are resting on sufficient rough inclined surface. Discuss the normal contact

force between them

O Level (Multiple choice Questions)

229. A round disc of moment of inertia I2 about its axis perpendicular to its plane and passing through its centre is

placed over another disc of moment of inertia I1 rotating with an angular velocity about the same axis. The

final angular velocity of the combination of discs id


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a)

1

21

I

II b)

21

1

II

I

c) d)

21

1

II

I

230. A solid sphere, a hollow sphere and a ring are released form top of an inclined plane (frictionless) so that they

slide down the plane. Then maximum acceleration down the plane is for (no rolling)

a) Solid sphere. b) Hollow sphere c) Ring d) All same

231. A particle of mass m moves along line PG with velocity v as shown. What is the angular momentum of the

particle about P?

a) mvL b) mvl c) mvr d) Zero

232. A circular disc X of radius R is made form an iron plate of thickness t and another disc Y of radius 4R is made

form an iron plate of thickness t/4. Then the relation between the M.I. Ix and Iy is

a) Iy = 32 Ix b) Iy = 16 Ix c) Iy = Ix d) Iy = 64 Ix

233. A ball rolls without slipping. The radius of gyration of the ball about an axis passing through its centre of mass

is k. If the radius of ball be R, then the fraction of total energy associated with its rotational energy will be

a)2

22

R

Rk b)

2

2

R

kc)

22

2

Rk

k

d)

22

2

Rk

R

234. A circular disc of radius R and thickness R/6 has moment of inertia. I. about an axis passing through its centre

and perpendicular to its plane. It is melted and recast into a solid sphere. The M.I. of the sphere about its

diameter as axis of rotation is

a) I b) 2I / 8 c) I / 5 d) I / 10

235. A heavy disc is thrown on a horizontal surface in such a way that it slides with speed v0 initially without

rolling. It will start rolling without slipping when its speed reduces to

a) v0 /2 b) 2v0 /5 c) 3 v0 /5 d) 5 v0 /7


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236. One quarter sector is cut from a uniform circular disc of radius R. This sector has mass M. It is made to rotate

about a line perpendicular to its plane and passing through its centre of the original disc. Its moment of inertia

about the axis of rotation is

a)2

2

1MR b)

2

4

1MR c)

2

8

1MR d)

22MR

237. A disc of mass M and radius R is rolling with angular speed on a horizontal plane as shown. The magnitude

of angular momentum of disc about the origin O is

a) 2

2

1MR b) 2MR c)

2

2

3MR d) 22MR

238. A cubical block of side a is moving with velocity v on the horizontal smooth plane as shown in fig. It hits a

ridge at point O. The angular speed of the block after it hits O is

a)a

v

4

3b)

a

v

2

3c)

a

v

2

3d) Zero

239. A particle of mass m is released form rest at point A falling parallel to vertical y-axis. Its angular momentum

after falling through distance h about O is


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a) ghma 2 b) gha

m2 c)

gh

mad)

ag

mh

240. A cylinder of radius R is spinned and then placed on an inclined having friction coefficient tan . The

cylinder continues to spin without falling for time

a)

sin3

0

g

Rb)

sin2

0

g

Rc)

sin

0

g

Rd)

sin

2 0

g

R

241. A point is moving in a circle. The ratio of its angular velocity about a point on thecircumference of the circle

and about the centre of circle is

a) 1 : 2 b) 2 : 1 c) 1: d) :1

242. A cylindrical drum is pushed along by a board of length l. The drum rolls forward on the ground a distance of

l/2. There is no slipping at any instant. During the process of pushing the board, the distance moved by the man

on the ground is

a) l/2 b) 3 l/2 c) l d) None of these

243. A string is wrapped around a cylinder of mass M and radius R. The string is pulled vertically upward to

prevent the centre of mass from falling as the cylinder unwinds the string. Find the length of the string

unwound when the cylinder has reached a speed .

a) g

R 22

b) g

R

2

22

c) g

R

4

22

d) g

R

8

22

244. A uniform ball of radius r rolls without slipping down from the top of sphere of radius R. The angular velocity

of the ball at the moment it breaks off the sphere will be (beglect initial velocity of ball)

a)

217

10

r

grR b)

2

10

7

r

grR c)

2

5

r

grR d)

2

5

2

r

grR


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245. A smooth rod of length lis kept inside a trolley at an angle as shown in the figure. What should be the

acceleration a of the trolley so that the rod remains in equilibrium with respect to it?

246. A solid body rotates about a stationary axis according to the law3

26 tt . What is the mean value of

angular velocity over the time interval between t = 0 and the time when the body comes to rest?

a) 2 rad/s b) 7 rad/s c) 3 rad/s d) 4 rad/s

247. A solid sphere of radius R is pulled by a force F acting at the top of the sphere as shown in the fig. There is no

slipping anywhere. Work done by force F, when the centre of mass moves a distances is

a) Fs b) 2 Fs c) Zero d)2

3Fs

248. The plank in the figure moves a distance 100mm to the right while the centre of mass of the sphere of radius

150mm moves distance 75mm to the left. The angular displacement of the sphere (in rad) is (assume there is

no slipping)

a)6

1b)

6

7c) 1 d)

2

1

249. A uniform rod of mass m is bent into the from of a semicircle of radius R. The M.I. of the rod about an axis

passing through A and perpendicular the the plane of the paper is


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250. Let be the M.I. of a uniform squire plate about an axis AB that passes through its centre and is parallel to two

of its edges. CD is a line in the plane of the plate that passes through the centre of plate and makes an angle

with AB. The M.I. of the plate about the axis CD is then equal to

a) I b) I 2sin c) I 2cos d) I 2/cos2

251. From the circular disc of radius R and mass M a concentric circular disc of small radius ris cut and removed,

the mass of which is m. The M.I. of the angular disc remaining about its axis perpendicular to the plane and

passing through the centre of mass will be

a) 222

1rRM b) 22

2

1rRm c) 22

2

1rRm d) 22

2

1mrMR

252. A mass M is moving with a constant velocity parallel to the x-axis. Its angular momentum with respect to

origin.

a) is zero b) remains constant c) goes on increasing d) goes on decreasing

253. A rod is hanging from a support. Find out the distance x from the point of suspension where force F (impulsive

force) is applied, so that no reaction force is applied by suppot.

a) 3

L

b) 3

2L

c) 4

L

d) 4

3L

254. A spherical solid body of mass m slips without friction down an inclined plane and reaches its bottom with

velocity v. Had this body been rolling down, then its velocity at the bottom would be

a) v

5

2b) 2v c)

2

1v d)

7

10v


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255. A hoop rolls on a horizontal ground without slipping with speed v. Speed of particle P on the circumference of

the hoop at angle as shown in figure is

a) 2/sin2 v b) 2/sinv c) 2/cos2 v d) 2/cosv

A Level (Multiple choice Questions)

256. A particle is moving in x-y plane. At certain instant of time, the components of its velocity and acceleration as

follows:22

/1,/4,/3 smasmvsmv yx . The note of change of speed of this moment is

a)2

/10 sm b) 4 m/s2 c)2

/5 sm d) 2 m/s2

257. Block A and C start form rest and move to the right with acceleration aA = 12t m/s2

and aC = 3 m/s2.

Here t is in seconds. The time when block B again comes to rest is

a) 2s b) 1s c) s2

3d) s

2

1

258. An elastic spring has a length l1, when tension in it 4N. Its length is l2 when tension in it is 5N. What will be its

length when tension in it is 9N?

a) 5l14l2 b) 5l24l1 c) 4l1 + 5l2 d) 4l2 + 5l1

259. Acceleration vs time graph of a particle moving in a straight line is a shown. If initially particle was at rest,

then corresponding KE vs time graph will be


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a) b) c) d)

260. Power supplied to a particle of mass 2kg varies with time as2

32t

P watt, here t is in sec. If velocity of

particle at t = 0 is v = 0. The velocity of particle at time t = 2sec will be

a) 1 m/s b) 4 m/s c) 2 m/s d) 22 m/s

261. Two billiard balls of the same size and mass are in contact on a billiard table. A third ball of the same size and

mass strikes them symmetrically and remains at rest after the impact. The coefficient of restitution between the

balls is

a) 1/2 b) 3/2 c) 2/3 d) 3/4

262. A constant power is supplied to a rotating disc. Angular velocity () of disc varies with number of rotations

(n) made by the disc as

a)3/1n b) 2/3n c) 3/2n d) 2n

263. Acceleration displacement graph of a particle executing SHM is as shown in fig. The time period of its

oscillation is (in see)

a) 2/ b) 2 c) d) 4/

264. Two sinusoidal waves of freq. f an f+ f traveling in same direction interfere with each other and

produce maxima at x = 0 and t = 0. At what time they again give maxima at x = 0?

a)f

1b)

f2

1c)

f3

1d)

f

2


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265. Two particles each of mass m and charge q are attached to the ends of a light rod of length 2R. The rod is

rotated at constant angular speed about a perpendicular axis passing through its centre. The ratio of the

magnitudes of the magnetic of the system and its angular momentum about the centre of rod is

a) mq 2/ b) mq / c) mq /2 d) mq /

266. Three gases He, O2 and CH4 undergo adiabatic process. The variation of temperature with volume is

a) b) c) d)

MECHANICS QUESTION BANK

1. In each of the following questions, find the unknown velocity / velocities. Assume that the thread is

inextensible and taut in each case.

a) b) c)

d) e)


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f) g) h)

i) j)

k) l)


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m) n)

o) p)

2. If the end of the cable at A is pulled down with a speed of 2 m/s, determine the speed at which block B rises.

3. If the end of the cable at A is pulled down with a speed of 2m/s, determine the speed at which block B rises.


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4. If the hydraulic cylinder at H draws in rod BC at 2 ft/s determine the speed of the slider at A.

5. The hoist is used lift the load at D. If the end A of the chain is traveling downward at vA = 5ft/s and the end B

is traveling upward at vB = 2ft/s, determine the velocity of the load at D.

6. If the end A of cable is moving upwards at vA = 14m/s, determine the speed of block B.


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7. Determine the velocity of block B at the instant when the velocity of block A is 16 in/s, directed upwards.

8. Block C is moving up at the constant speed of 6 in/s. Given that the elevations of blocks A and B are always

equal, determine the velocity of B.

9. The pulley arrangement shown is designed for hosing materials. If BC remains fixed while the plunger P is

pushed downward with a speed of 1 m/s, determine the speed of the load at A.


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10. In each of the following cases, some blocks are attached to some motor/s through ideal threads and pullies. The

motors are giving out/taking in the threads at the rates shown in the figure. Find the unknown velocity in each

case. The blocks are moving such that threads are always taut.

a) b)

c) d) f)

g)

11. Determine the time needed for the load at B to attain a speed of 8 m/s, starting from rest, if the cable is drawn

into the motor with an acceleration of 0.2 m/s2.


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12. Determine the constant speed at which the cable at A must be drawn in by the motor in order to raise the load

6m in 1.5s.

13. Staring form rest, the cable can be wound onto the drum of the motor at a rate of vA = (3t2) m/s, where t is in

seconds. Determine the time needed to lift the load 7m. [use of the figure of previous problem]

14. The cylinder C is being lifted using the cable and pully system as shown. If point A on the cable is being

drawn toward the drum with a speed of 2m/s, determine the speed of the cylinder.

15. The cylinder C can be lifted with a maximum acceleration of ac =3 m/s2 without causing the cables to fail.

Determine the speed at which point A is moving toward the drum when S = 4m if the cylinder is lifted from

rest. In the shortest time possible. [use of the figure of previous problem]


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16. The motor at C pulls in the cable with an acceleration aC = (3t2) m/s2, where t is in second. The motor at D

drawn in its cable at aD = 5m/s2. If both motors start at the same instant form rest when d = 3m, determine (a)

the time needed for d = 0 and (b) the relative velocity of block A with respect to block B when this occur.

17. The motor draws in the cable at C with a constant velocity of vC = 4m/s. The motor draws in the cable at D

with a constant acceleration of aD = 8m/s2. If vD = 0 when t = 0, determine (a) the time needed for block A to

rise 3m, and (b) the relative velocity of block A with respect to block B when this occurs

18. If motors at A and B draw in their attached cables with an acceleration of a = (0.2t) m/s2, where i is in seconds,

determine the speed of the block when it reaches a height of h = 4m, starting from rest. Also, how much time

does it take to reach this height?


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19. The mine car C is being pulled up the incline using the motor M and the rope-and-pulley arrangement shown.

Determine the speed vp at which a point P on the cable must be traveling toward the motor to move the car up

the plane with a constant speed of v = 2m/s.

20. Each of the following problems shows some blocks attached to each other through ideal strings. Find the

unknown velocity at the instant shown in the figure.

a) b) c)

d

Motion Question Bank for IIT JEE

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