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Rotational Mechanics — JEE Main & Advanced Physics PYQs

158 previous year questions from Rotational Mechanics with answers and solutions. Numbered list, year tags, and one-tap solutions — built for serious JEE / NEET practice.

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1

A wheel revolves about its axis with a uniform angular acceleration. Beginning from rest, it attains 100 rev/sec in 4 seconds. Determine the angular acceleration and the angle rota

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2

Starting from rest, a wheel is uniformly accelerated at 4 rad/s ^2 for 10 seconds. Subsequently, it rotates uniformly for the next 10 seconds, and is finally brought to rest over t

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3

Determine the angular velocity of a body rotating with an acceleration of 2 rev/s ^2 as it completes the 5 th revolution after starting.

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4

A body rotates about a fixed axis with an angular acceleration of one radian/second/second . Determine the angle through which it rotates during the time in which its angular veloc

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5

A disc of radius 10 cm rotates about its axis with an angular speed of 20 rad/s . Determine the linear speed of a point situated on the rim.

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6

A disc of radius 10 cm rotates about its axis with an angular speed of 20 rad/s . Determine the linear speed of the middle point of a radius.

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7

A disc rotates about its axis with a uniform angular acceleration of 4 rad/s ^2 . Determine the radial and tangential accelerations of a particle located 1 cm from the axis at the

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8

A block is suspended from a string wrapped on a disc of radius 20 cm , which is free to rotate about its fixed horizontal axis. If the angular speed of the disc is 10 rad/s at a pa

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9

Three particles, each having a mass of 200 g , are placed at the corners of an equilateral triangle with a side length of 10 cm . Determine the moment of inertia of the system abou

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10

Three particles, each having a mass of 200 g , are placed at the corners of an equilateral triangle with a side length of 10 cm . Determine the moment of inertia of the system abou

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11

Determine the moment of inertia of a pair of spheres, each possessing a mass m and radius r , placed in contact, about the tangent passing through their point of contact.

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12

Particles having masses of 1 g , 2 g , 3 g , ..., 100 g are placed at the marks 1 cm , 2 cm , 3 cm , ..., 100 cm respectively on a metre scale. Determine the moment of inertia of t

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13

A uniform rod with a mass of 0.50 kg and a length of 1 m has a moment of inertia of 0.10 kg-m ^2 about an axis perpendicular to it. Determine the distance from this axis to the mid

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14

Determine the radius of gyration of a circular ring of radius r about a line perpendicular to the ring's plane and passing through one of its particles.

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15

A uniform disc has a radius of gyration equal to its radius r about a line perpendicular to the disc. Determine the distance of this line from the centre.

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16

Determine the moment of inertia of a uniform square plate having mass m and edge a about one of its diagonals.

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17

The surface density (mass/area) of a circular disc having a radius a varies with the distance from the centre according to (r) = A + Br . Determine its moment of inertia about a li

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18

A particle of mass m is launched with a speed u at an angle relative to the horizontal. Determine the magnitude of the torque of the particle's weight about the point of projection

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19

A simple pendulum of length l is displaced to form an angle heta with the vertical. Calculate the magnitude of the torque exerted by the weight w of the bob about the point of susp

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20

Calculate the total torque acting on the body shown in the figure about the point O .

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21

A force of 6.0 N applied at 30^ to a wrench at a distance of 8 cm from the nut is just sufficient to loosen the nut. Determine the force F that would be required to loosen it if it

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22

A cubical block of mass m and edge length a is sliding down a rough inclined plane of inclination heta at a uniform speed. Determine the torque of the normal force exerted on the b

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23

A square plate having a mass of 120 g and an edge of 5.0 cm rotates about one of its edges. Determine the torque acting on the plate if it undergoes a uniform angular acceleration

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24

A horizontal rod of mass m and length L is free to rotate about a vertical axis passing through its centre. A constant horizontal force of magnitude F acts on the rod at a distance

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25

A square plate of mass 120 ext g and edge 5.0 ext cm has a uniform angular acceleration of 0.2 ext rad/s ^2 . Calculate the torque on the plate if it rotates about a diagonal with

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26

A flywheel with a moment of inertia of 5.0 kg-m ^2 is rotated at a speed of 60 rad/s . Due to friction at the axle, it comes to rest in 5.0 minutes . Determine the average torque o

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27

A flywheel with a moment of inertia of 5.0 kg-m ^2 is rotated at a speed of 60 rad/s . Due to friction at the axle, it comes to rest in 5.0 minutes . Determine the total work done

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28

A flywheel with a moment of inertia of 5.0 kg-m ^2 is rotated at a speed of 60 rad/s . Due to friction at the axle, it comes to rest in 5.0 minutes . Determine the angular momentum

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29

Due to friction between ocean water and the earth's surface, the rotational kinetic energy of the earth continuously decreases. Determine the average torque of friction on the eart

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30

A wheel rotating with uniform angular acceleration completes 50 revolutions in the first five seconds after starting. Determine the angular acceleration and the angular velocity at

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31

A wheel rotating about its axis at a speed of 600 rpm (revolutions per minute) is brought to rest by applying a constant torque for 10 seconds. Determine the angular deceleration a

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32

A cylinder rotating at an angular speed of 50 rev/s is brought into contact with an identical stationary cylinder. Due to kinetic friction, torques act on the two cylinders, accele

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33

A wheel of mass 10 kg and radius 20 cm is spinning at an angular speed of 100 rev/min when the motor is switched off. Ignoring friction at the axle, determine the force that must b

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34

A body rotating at 20 rad/s is subjected to a constant torque that provides a deceleration of 2 rad/s ^2 . If the torque continues to act, at what time will the body possess a kine

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35

A light rod of length 1 m is pivoted at its centre, with two masses of 5 kg and 2 kg suspended from its ends, as shown in the figure. Determine the initial angular acceleration of

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36

A rod of length 1 m is pivoted at its centre. Two masses of 5 kg and 2 kg hang from its ends as shown in the figure. The rod itself has a mass of 1 kg distributed uniformly along i

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37

As depicted in the figure, two blocks of masses m and M are linked by a string that passes over a pulley. The horizontal table on which the mass m slides is smooth. The pulley, whi

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38

A string is wound around a wheel having a moment of inertia of 0.20 kg-m ^2 and a radius of 10 cm . The string then passes over a light pulley to suspend a block of mass 2.0 kg , a

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39

A string is wrapped on a wheel of moment of inertia 0.20 kg-m ^2 and radius 10 cm and goes through a pulley to support a block of mass 2.0 kg as shown in the figure. The smaller pu

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40

In the arrangement shown in the figure, the two identical pulleys each have a radius R and a moment of inertia I . Calculate the acceleration of the block M .

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41

The descending pulley shown in the figure has a radius 20 cm and moment of inertia 0.20 kg-m ^2 . The fixed pulley is light and the horizontal plane frictionless. Find the accelera

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42

Consider the pulley shown in the figure, which has a radius of 10 cm and a moment of inertia of 0.5 kg-m ^2 about its axis. Assuming that the inclined planes are frictionless, dete

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43

A pulley of radius 10 cm and moment of inertia 0.5 kg-m ^2 connects two blocks of masses 4.0 kg and 2.0 kg on inclined planes as shown. The plane beneath the 2.0 kg block has coeff

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44

A uniform metre stick of mass 200 g is suspended from the ceiling by two vertical strings of equal lengths attached at its ends. A small object of mass 20 g is positioned on the st

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45

A uniform ladder of length 10.0 m and mass 16.0 kg rests against a frictionless vertical wall, forming an angle of 37^ with the wall. The ground is rough. An electrician weighing 6

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46

A uniform ladder of length 10.0 m and mass 16.0 kg rests against a frictionless vertical wall, making an angle of 37^ with it. The ground is rough. A mechanic stands on the ladder

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47

A 6.5 m long ladder rests against a vertical wall, reaching a height of 6.0 m . A 60 kg man stands halfway up the ladder. Determine the torque of the force exerted by the man on th

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48

A 6.5 m long ladder rests against a vertical wall, reaching a height of 6.0 m . A 60 kg man stands halfway up the ladder. Assuming the weight of the ladder to be negligible as comp

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49

An almirah door is 6 ft high and 1.5 ft wide, weighing 8 kg . It is held up by two hinges placed 1 ft from its ends. Assuming the magnitudes of the forces exerted by the hinges on

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50

A uniform rod of length L rests against a smooth roller, as shown in the figure. Determine the friction coefficient between the ground and the lower end, given that the minimum ang

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51

A uniform rod having a mass of 300 g and a length of 50 cm rotates at a uniform angular speed of 2 rad/s about an axis perpendicular to the rod through one end. Calculate the angul

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52

A uniform rod having a mass of 300 g and a length of 50 cm rotates at a uniform angular speed of 2 rad/s about an axis perpendicular to the rod through one end. Determine the speed

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53

A uniform rod having a mass of 300 g and a length of 50 cm rotates at a uniform angular speed of 2 rad/s about an axis perpendicular to the rod through one end. Compute the kinetic

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54

Subjected to a constant torque of 0.10 N-m , a uniform square plate of mass 2.0 kg and edge 10 cm rotates about one of its diagonals. Determine the angular momentum and the kinetic

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55

Determine the ratio of the earth's angular momentum about its axis due to its spinning motion to its angular momentum about the sun due to its orbital motion. The radius of the ear

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56

Two particles of masses m₁ and m₂ are connected by a light rigid rod of length r . The system rotates at an angular speed about an axis passing through the centre of mass of the sy

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57

Two identical small balls, each having a mass of 1/2 kg , are attached to the ends of a light rod that is 50 cm long to form a dumb-bell. This dumb-bell rotates at an angular speed

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58

A wheel having a moment of inertia of 0.500 kg-m ^2 and a radius of 20.0 cm is rotating about its axis with an angular speed of 20.0 rad/s . It picks up a stationary particle of ma

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59

A diver with a moment of inertia of 6.0 kg-m ^2 about an axis passing through his centre of mass rotates about this axis at an angular speed of 2 rad/s . If the diver folds his han

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60

A boy sits in a revolving chair that rotates at an angular speed of 120 revolutions per minute. Two heavy balls are part of the revolving system, and the boy can pull the balls clo

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61

A wheel with a moment of inertia of 0.10 kg-m ^2 rotates about a shaft at an angular speed of 160 rev/minute . A second wheel is set into rotation at 300 rev/minute and is then cou

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62

A boy stands on a platform that can freely rotate about its vertical axis. He is holding an open umbrella, with the umbrella's axis coinciding with that of the platform. The moment

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63

A kid of mass M stands at the edge of a platform of radius R which can rotate freely about its axis. The moment of inertia of the platform is I . The system is initially at rest, a

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64

A kid of mass M stands at the edge of a platform of radius R , which is free to rotate about its axis. The moment of inertia of the platform is I . The system is initially at rest

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65

A kid of mass M stands at the edge of a platform of radius R which can rotate freely about its axis. The moment of inertia of the platform is I . The system is rotating anticlockwi

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66

A uniform rod of mass m and length l is struck at one end by a force F perpendicular to the rod for a short duration t . Assuming t is small enough that the rod does not appreciabl

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67

A uniform rod of mass m and length l is struck at one end by a force F perpendicular to the rod for a brief time interval t . Assuming that t is so small that the rod does not noti

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68

A uniform rod of mass m and length l is struck at one end by a force F perpendicular to the rod for a short time interval t . Assuming t is so brief that the rod does not appreciab

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69

A uniform rod of mass m and length l is struck at one end by a force F perpendicular to the rod for a short duration t . Assuming that t is so small that the rod does not appreciab

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70

A uniform rod of length L rests on a smooth horizontal table. A particle moving on the table perpendicularly strikes the rod at one end and stops. Determine the distance travelled

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71

A uniform rod of length L and mass M lies on a smooth horizontal table. A particle of mass m moving on the table strikes the rod perpendicularly at one end with speed v and sticks

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72

Two small balls A and B , each having mass m , are rigidly connected by a light horizontal rod of length L . The rod is clamped at its centre such that it can freely rotate about a

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73

Two small balls A and B , each having mass m , are rigidly attached to the ends of a light rod of length L as depicted in the figure. On a frictionless horizontal surface, the syst

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74

Two small balls A and B , each having mass m , are rigidly connected to the ends of a light rod of length L . The system translates on a frictionless horizontal surface with a velo

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75

Two small balls A and B , each with mass m , are rigidly attached to the ends of a light rod of length L . Over a frictionless horizontal surface, the system translates with a velo

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76

Two small balls A and B , each of mass m , are joined rigidly to the ends of a light rod of length L as shown. The rod is clamped at its centre so that it can rotate freely about a

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77

Two blocks having masses of 400 g and 200 g are connected by a light string passing over a pulley that is free to rotate about its axis. The pulley possesses a moment of inertia of

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78

Two blocks having masses of 400 g and 200 g are connected by a light string passing over a pulley that is free to rotate about its axis. The pulley possesses a moment of inertia of

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79

As illustrated in the figure, a pulley possesses a radius of 20 cm and a moment of inertia of 0.2 kg-m ^2 . A string passing over it connects to a vertical spring (spring constant

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80

A metre stick is positioned vertically with one end resting on a rough horizontal floor. It is gently released to fall onto the floor. Assuming the end on the floor does not slip,

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81

Pivoted at its upper end, a metre stick weighing 240 g is able to freely rotate in a vertical plane through this end, as shown in the figure. A particle of mass 100 g is attached t

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82

A uniform rod, pivoted at its upper end, hangs vertically. It is displaced by an angle of 60^ and subsequently released. Determine the magnitude of the force acting on a particle o

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83

A cylinder is rolling on a horizontal plane surface. Given that the speed of its centre is 25 m/s , determine the speed of its highest point.

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84

A string is wrapped around the edge of a uniform disc, and its free end is attached to the ceiling. The disc descends, unwinding the string. Determine the downward acceleration of

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85

A sphere of mass m rolls along a plane surface. Determine its kinetic energy at an instant when its centre travels with speed v .

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86

A small spherical ball is released from a height h on the rough track shown in the figure. Assuming no slipping occurs anywhere, determine its linear speed as it rolls along the ho

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87

A sphere begins rolling down an incline with an inclination . Determine the speed of its centre once it has travelled a distance l .

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88

A rough track is shown in the figure. A small disc is set rolling without slipping with speed v on the horizontal part of the track from right to left. To what height will it climb

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89

A hollow sphere is released from the top of an inclined plane of inclination . Determine the minimum coefficient of friction between the sphere and the plane required to prevent sl

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90

A solid sphere of mass m is released from rest at the rim of a hemispherical cup such that it rolls down the surface. Given that the rim of the hemisphere is kept horizontal, deter

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91

As depicted in the figure, a rough track features a portion shaped like a cylinder of radius R . Find the minimum linear speed at which a sphere of radius r should be set rolling o

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92

As shown in the figure, a small spherical ball of mass m rolls down a loop track. The ball is released on the linear portion at a vertical height H from the lowest point. The circu

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93

A small spherical ball of mass m rolls down a loop track. The ball is released on the linear portion at a vertical height H from the lowest point. The circular part shown has a rad

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94

A small spherical ball of mass m rolls down a loop track. The ball is released on the linear portion at a vertical height H from the lowest point. The circular part shown has a rad

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95

A thin spherical shell of radius R , resting on a rough horizontal surface, is struck sharply and horizontally by a cue. Where should it be struck so that the shell does not slip o

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96

A uniform wheel of radius R is made to rotate about its axis at an angular speed . The rotating wheel is then placed on a rough horizontal surface, keeping its axis horizontal. Due

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97

A thin spherical shell resting on a rough horizontal surface is struck by a cue such that the line of action passes through the shell's centre. Consequently, the shell begins trans

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98

A hollow sphere of radius R rests on a smooth horizontal surface. It is pulled by a horizontal force acting tangentially at the highest point. Determine the distance travelled by t

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99

A solid sphere of mass 0.50 kg rests on a horizontal surface. The coefficient of static friction between the sphere and the surface is 2/7 . Determine the maximum horizontal force

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100

As shown in the figure, a solid sphere is set into motion on a rough horizontal surface, possessing a forward linear speed v and an anticlockwise angular speed v/R . Determine the

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101

A solid sphere is set into motion on a rough horizontal surface, possessing a forward linear speed v and an anticlockwise angular speed v/R . Determine the linear speed of the sphe

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102

A solid sphere rolling on a rough horizontal surface with a linear speed v elastically collides with a fixed, smooth, vertical wall. Determine the speed of the sphere after it comm

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103

A particle travels with a constant velocity parallel to the X -axis. Its angular momentum relative to the origin

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104

Suppose A represents a unit vector directed along the axis of rotation of a purely rotating body, and B is a unit vector directed along the velocity of a particle P of the body sit

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105

A body executes pure rotation. The angular velocity of the body, the distance r of a particle from the axis, and the linear speed v of the particle satisfy the relation = v r . The

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106

A body rotates uniformly about a fixed vertical axis in an inertial frame. The resultant force acting on a particle of the body not situated on the axis is

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107

A body rotates uniformly about an axis fixed in an inertial frame of reference. Let A be a unit vector along the rotation axis and B be a unit vector along the resultant force acti

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108

Consider a force F that acts on a particle with position vector r . If represents the torque of this force about the origin, which of the following is true?

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109

A uniform rod of mass m and length l has one end clamped. It rests on a smooth horizontal surface, rotating about the clamped end with a uniform angular velocity . The horizontal c

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110

A uniform rod is kept vertically at a point O on a smooth horizontal surface. After being slightly rotated and released, it falls onto the horizontal surface. The lower end will be

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111

A circular disc A of radius r is fabricated from an iron plate of thickness t , and a second circular disc B of radius 4r is fabricated from an iron plate of thickness t/4 . The re

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112

Two circular discs A and B are made of the same material. Disc A has radius r and thickness t , while disc B has radius 4r and thickness t/4 . Equal torques act on both discs, init

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113

As illustrated in the figure, a small wheel is fixed coaxially onto a larger wheel of double the radius. The entire system rotates about their common axis. The strings supporting A

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114

A closed cylindrical tube, which contains some water but is not completely filled, rests in a horizontal plane. When the tube is rotated about its perpendicular bisector, the momen

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115

Determine the moment of inertia for a uniform semicircular wire of mass M and radius r , taken about an axis passing through its centre and perpendicular to its plane.

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116

Consider a body whose centre of mass is situated at the origin, with three of its particles located at (a, 0, 0) , (0, a, 0) , and (0, 0, a) . The moments of inertia of this body a

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117

A body rotates nonuniformly about a fixed vertical axis within an inertial frame. The resultant force acting on a particle of the body that is not located on the axis is

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118

A cubical block of mass M and edge length a slides down a rough inclined plane of inclination heta at a uniform velocity. Determine the magnitude of the torque produced by the norm

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119

A thin circular ring having mass M and radius r rotates about its axis with an angular speed . Subsequently, two particles, each of mass m , are attached at diametrically opposite

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120

A person sitting securely on a rotating stool has his arms extended. If he folds his arms, what happens to his angular momentum about the axis of rotation?

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