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Rotational Motion — JEE Main & Advanced Physics PYQs

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

632 questionsPhysicsSolutions on every page
1

Consider a large disk of radius R and two smaller disks, each of radius r = R/50 , lying on its circumference, as shown in the figure. The smaller disks are initially in contact wi

JEE Advanced 2026 Solution View → 2

A solid cylinder of radius R rolls without slipping with a center of mass speed v₀ = gR 3 on a horizontal surface with a vertical edge, as shown in the figure. Here, g is the accel

JEE Advanced 2026 Solution View → 3

List-I shows four planar structures made of uniform solid rods each of mass m and length l . In the List-II the possible moment of inertia of these structures about an axis OCO' ,

JEE Advanced 2026 Solution View → 4

Passage: A uniform circular disk of radius 0.2 m and mass 1 kg is pivoted at its top point C such that it can rotate freely around C in the XY plane, as shown in the figure. Initia

JEE Advanced 2026 Solution View → 5

Passage: A uniform circular disk of radius 0.2 m and mass 1 kg is pivoted at its top point C such that it can rotate freely around C in the XY plane, as shown in the figure. Initia

JEE Advanced 2026 Solution View → 6

A solid cylinder having radius R and length L is slipping on a rough horizontal plane. At time t=0 the cylinder has a translational velocity v₀=49 m/s, perpendicular to its axis an

JEE Main 2026 Solution View → 7

A solid sphere ( A ) of mass 5m and a spherical shell ( B ) of mass m , both having same radius, are placed on a rough surface. When a force of same magnitude is applied tangential

JEE Main 2026 Solution View → 8

A solid sphere of radius 4 cm and mass 5 kg is rotating (rotation axis is passing through the centre of the sphere) with an angular velocity of 1200 rpm. It is brought to rest in 1

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A wheel initially at rest is subjected to a uniform angular acceleration about its axis. In the first 2 s it rotates through an angle ₁ and in the next 2 s it rotates through an an

JEE Main 2026 Solution View → 10

An object of uniform density rolls up the curved path with the initial velocity v₀ as shown in the figure. If the maximum height attained by an object is 7v₀^2 10g ( g = accelerati

JEE Main 2026 Solution View → 11

A solid sphere of mass M and radius R is divided into two unequal parts. The smaller part having mass M/8 is converted into a sphere of radius r and the larger part is converted in

JEE Main 2026 Solution View → 12

Moment of inertia about an axis AB for a rod of mass 40 kg and length 3 m is same as that of a solid sphere of mass of 10 kg and radius R about an axis parallel to AB axis with sep

JEE Main 2026 Solution View → 13

A particle is rotating in a circular path and at any instant its motion can be described as = 5t^4 40 - t^3 3 . The angular acceleration of the particle after 10 seconds is _______

JEE Main 2026 Solution View → 14

When the position vector r =x i +y j +z k changes sign as - r , which one of the following vector will not flip under sign change ?

JEE Main 2026 Solution View → 15

A fly wheel having mass 3 kg and radius 5 m is free to rotate about a horizontal axis. A string having negligible mass is wound around the wheel and the loose end of the string is

JEE Main 2026 Solution View → 16

Two circular discs of radius each 10 cm are joined at their centres by a rod of length 30 cm and mass 600 gm as shown in figure. If the mass of each disc is 600 gm and applied torq

JEE Main 2026 Solution View → 17

A solid sphere of radius 10 cm is rotating about an axis which is at a distance 15 cm from its centre. The radius of gyration about this axis is n ~cm . The value of n is

JEE Main 2026 Solution View → 18

A thin uniform rod (X) of mass M and length L is pivoted at a height ( L 3 ) as shown in the figure. The rod is allowed to fall from a vertical position and lie horizontally on the

JEE Main 2026 Solution View → 19

A uniform solid cylinder of length L and radius R has moment of inertia about its axis equal to I₁ . A small co-centric cylinder of length L / 2 and radius R / 3 carved from this c

JEE Main 2026 Solution View → 20

Two masses 400 g and 350 g are suspended from the ends of a light string passing over a heavy pulley of radius 2 cm. When released from rest the heavier mass is observed to fall 81

JEE Main 2026 Solution View → 21

Suppose there is a uniform circular disc of mass M ~kg and radius r ~m shown in figure. The shaded regions are cut out from the disc. The moment of inertia of the remainder about t

JEE Main 2026 Solution View → 22

Two small balls with masses m and 2 m are attached to both ends of a rigid rod of length d and negligible mass. If angular momentum of this system is L about an axis ( A ) passing

JEE Main 2026 Solution View → 23

The moment of inertia of a square loop made of four uniform solid cylinders, each having radius R and length L( R < L ) about an axis passing through the mid points of opposite sid

JEE Main 2026 Solution View → 24

A uniform bar of length 12 cm and mass 20 m lies on a smooth horizontal table. Two point masses m and 2 m are moving in opposite directions with same speed of v and in the same pla

JEE Main 2026 Solution View → 25

Two masses m and 2 m are connected by a light string going over a pulley (disc) of mass 30 m with radius r=0.1 ~m . The pulley is mounted in a vertical plane and it is free to rota

JEE Main 2026 Solution View → 26

A solid sphere of mass 5 kg and radius 10 cm is kept in contact with another solid sphere of mass 10 kg and radius 20 cm. The moment of inertia of this pair of spheres about the ta

JEE Main 2026 Solution View → 27

A circular disc has radius R₁ and thickness T₁ . Another circular disc made of the same material has radius R₂ and thickness T₂ . If the moment of inertia of both discs are same an

JEE Main 2026 Solution View → 28

The pulley shown in figure is made using a thin rim and two rods of length equal to diameter of the rim. The rim and each rod have a mass of M . Two blocks of mass of M and m are a

JEE Main 2026 Solution View → 29

Two cars A and B each of mass 10³ ~kg are moving on parallel tracks separated by a distance of 10 m, in same direction with speeds 72 ~km / h and 36 ~km / h . The magnitude of angu

JEE Main 2026 Solution View → 30

A uniform rod of mass m and length l suspended by means of two identical inextensible light strings as shown in figure. Tension in one string immediately after the other string is

JEE Main 2026 Solution View → 31

Two identical thin rods of mass M ~kg and length L ~m are connected as shown in figure. Moment of inertia of the combined rod system about an axis passing through point P and perpe

JEE Main 2026 Solution View → 32

A rod of linear mass density ' ' and length ' L ' is bent to form a ring of radius 'R'. Moment of inertia of ring about any of its diameter is :

JEE Main 2025 Solution View → 33

A thin solid disk of 1 kg is rotating along its diameter axis at the speed of 1800 rpm. By applying an external torque of 25 Nm for 40 s, the speed increases to 2100 rpm. The diame

JEE Main 2025 Solution View → 34

A cube having a side of 10 cm with unknown mass and 200 gm mass were hung at two ends of an uniform rigid rod of 27 cm long. The rod along with masses was placed on a wedge keeping

JEE Main 2025 Solution View → 35

M and R be the mass and radius of a disc. A small disc of radius R / 3 is removed from the bigger disc as shown in figure. The moment of inertia of remaining part of bigger disc ab

JEE Main 2025 Solution View → 36

A , B and C are disc, solid sphere and spherical shell respectively with same radii and masses. These masses are placed as shown in figure. The moment of inertia of the given syste

JEE Main 2025 Solution View → 37

A solid sphere with uniform density and radius R is rotating initially with constant angular velocity ( ₁ ) about its diameter. After some time during the rotation its starts loosi

JEE Main 2025 Solution View → 38

A wheel is rolling on a plane surface. The speed of a particle on the highest point of the rim is 8 ~m / s . The speed of the particle on the rim of the wheel at the same level as

JEE Main 2025 Solution View → 39

Which of the following are correct expression for torque acting on a body? B. = d dt ( r p ) C. = r d p dt D. = I E. = r F ( r = position vector; p = linear momentum; L = angular m

JEE Main 2025 Solution View → 40

If L and P represent the angular momentum and linear momentum respectively of a particle of mass ' m ' having position vector r = a ( i t + j t ) . The direction of force is

JEE Main 2025 Solution View → 41

A circular ring and a solid sphere having same radius roll down on an inclined plane from rest without slipping. The ratio of their velocities when reached at the bottom of the pla

JEE Main 2025 Solution View → 42

A force of 49 N acts tangentially at the highest point of a sphere (solid) of mass 20 kg , kept on a rough horizontal plane. If the sphere rolls without slipping, then the accelera

JEE Main 2025 Solution View → 43

The moment of inertia of a circular ring of mass M and diameter r about a tangential axis lying in the plane of the ring is :

JEE Main 2025 Solution View → 44

A wheel of radius 0.2 m rotates freely about its center when a string that is wrapped over its rim is pulled by force of 10 N as shown in figure. The established torque produces an

JEE Main 2025 Solution View → 45

Moment of inertia of a rod of mass ' M ' and length 'L' about an axis passing through its center and normal to its length is ' '. Now the rod is cut into two equal parts and these

JEE Main 2025 Solution View → 46

A square Lamina OABC of length 10 cm is pivoted at 'O'. Forces act at Lamina as shown in figure. If Lamina remains stationary, then the magnitude of F is :

JEE Main 2025 Solution View → 47

A cord of negligible mass is wound around the rim of a wheel supported by spokes with negligible mass. The mass of wheel is 10 kg and radius is 10 cm and it can freely rotate witho

JEE Main 2025 Solution View → 48

Three equal masses m are kept at vertices (A, B, C) of an equilateral triangle of side a in free space. At t=0 , they are given an initial velocity V _A=V₀ A C , V _B=V₀ B A and V

JEE Main 2025 Solution View → 49

The coordinates of a particle with respect to origin in a given reference frame is ((1,1,1) ) meters. If a force of ( F = i - j + k ) acts on the particle, then the magnitude of to

JEE Main 2025 Solution View → 50

Two iron solid discs of negligible thickness have radii R₁ and R₂ and moment of intertia I₁ and I₂ , respectively. For R₂=2 R₁ , the ratio of I₁ and I₂ would be 1 / x , where x = _

JEE Main 2025 Solution View → 51

The moment of inertia of a solid disc rotating along its diameter is 2.5 times higher than the moment of inertia of a ring rotating in similar way. The moment of inertia of a solid

JEE Main 2025 Solution View → 52

A solid sphere and a hollow sphere of the same mass and of same radius are rolled on an inclined plane. Let the time taken to reach the bottom by the solid sphere and the hollow sp

JEE Main 2025 Solution View → 53

A solid sphere is rolling without slipping on a horizontal plane. The ratio of the linear kinetic energy of the centre of mass of the sphere and rotational kinetic energy is :

JEE Main 2025 Solution View → 54

A uniform solid cylinder of mass ' m ' and radius ' r ' rolls along an inclined rough plane of inclination 45^ . If it starts to roll from rest from the top of the plane then the l

JEE Main 2025 Solution View → 55

An object of mass ' m ' is projected from origin in a vertical x y plane at an angle 45^ with the x axis with an initial velocity v ₀ . The magnitude and direction of the angular m

JEE Main 2025 Solution View → 56

A circular disk of radius R meter and mass M kg is rotating around the axis perpendicular to the disk. An external torque is applied to the disk such that (t)=5 t^2-8 t , where (t)

JEE Main 2025 Solution View → 57

A solid sphere of mass ' m ' and radius ' r ' is allowed to roll without slipping from the highest point of an inclined plane of length ' L ' and makes an angle 30^ with the horizo

JEE Main 2025 Solution View → 58

The torque due to the force (2 i + j +2 k ) about the origin, acting on a particle whose position vector is ( i + j + k ) , would be

JEE Main 2025 Solution View → 59

A uniform circular disc of radius ' R ' and mass ' M ' is rotating about an axis perpendicular to its plane and passing through its centre. A small circular part of radius R / 2 is

JEE Main 2025 Solution View → 60

The position vectors of two 1 kg particles, (A) and (B), are given by r _ A = ( ₁ t ^2 i + ₂ t j + ₃ t k ) m and r _ B = ( ₁ t i + ₂ t ^2 j + ₃ t k ) m , respectively; ( ₁=1 ~m / s

JEE Main 2025 Solution View → 61

A disc of mass M and radius R is free to rotate about its vertical axis as shown in the figure. A battery operated motor of negligible mass is fixed to this disc at a point on its

JEE Advanced 2024 Solution View → 62

A thin uniform rod of length L and certain mass is kept on a frictionless horizontal table with a massless string of length L fixed to one end (top view is shown in the figure). Th

JEE Advanced 2024 Solution View → 63

A circular disc reaches from top to bottom of an inclined plane of length l . When it slips down the plane, if takes t ~s . When it rolls down the plane then it takes ( 2 )^ 1 / 2

JEE Main 2024 Solution View → 64

A heavy iron bar, of weight W is having its one end on the ground and the other on the shoulder of a person. The bar makes an angle with the horizontal. The weight experienced by t

JEE Main 2024 Solution View → 65

A string is wrapped around the rim of a wheel of moment of inertia 0.40 kgm ^2 and radius 10 ~cm . The wheel is free to rotate about its axis. Initially the wheel is at rest. The s

JEE Main 2024 Solution View → 66

A thin circular disc of mass M and radius R is rotating in a horizontal plane about an axis passing through its centre and perpendicular to its plane with angular velocity . If ano

JEE Main 2024 Solution View → 67

A block is simply released from the top of an inclined plane as shown in the figure above. The maximum compression in the spring when the block hits the spring is :

JEE Main 2024 Solution View → 68

Three balls of masses 2 ~kg , 4 ~kg and 6 ~kg respectively are arranged at centre of the edges of an equilateral triangle of side 2 ~m . The moment of intertia of the system about

JEE Main 2024 Solution View → 69

If the radius of earth is reduced to three-fourth of its present value without change in its mass then value of duration of the day of earth will be ______ hours 30 minutes.

JEE Main 2024 Solution View → 70

A hollow sphere is rolling on a plane surface about its axis of symmetry. The ratio of rotational kinetic energy to its total kinetic energy is x 5 . The value of x is _____ .

JEE Main 2024 Solution View → 71

Ratio of radius of gyration of a hollow sphere to that of a solid cylinder of equal mass, for moment of Inertia about their diameter axis AB as shown in figure is 8 / x . The value

JEE Main 2024 Solution View → 72

A solid sphere and a hollow cylinder roll up without slipping on same inclined plane with same initial speed v . The sphere and the cylinder reaches upto maximum heights h₁ and h₂

JEE Main 2024 Solution View → 73

A disc of radius R and mass M is rolling horizontally without slipping with speed v . It then moves up an inclined smooth surface as shown in figure. The maximum height that the di

JEE Main 2024 Solution View → 74

A ball of mass 0 . 5 kg is attached to a string of length 50 cm . The ball is rotated on a horizontal circular path about its vertical axis. The maximum tension that the string can

JEE Main 2024 Solution View → 75

Two identical spheres each of mass 2 kg and radius 50 cm are fixed at the ends of a light rod so that the separation between the centers is 150 cm . Then, moment of inertia of the

JEE Main 2024 Solution View → 76

A body of mass m is projected with a speed u making an angle of 45 o with the ground. The angular momentum of the body about the point of projection, at the highest point is expres

JEE Main 2024 Solution View → 77

Two discs of moment of inertia I 1 = 4 kg m 2 and I 2 = 2 kg m 2 about their central axes & normal to their planes, rotating with angular speeds 10 rad s - 1 & 4 rad s - 1 respecti

JEE Main 2024 Solution View → 78

Consider a disc of mass 5 kg , radius 2 m , rotating with angular velocity of 10 rad s - 1 about an axis perpendicular to the plane of rotation. An identical disc is kept gently ov

JEE Main 2024 Solution View → 79

A body of mass 5 kg moving with a uniform speed 3 2 m s - 1 in X - Y plane along the line y = x + 4 . The angular momentum of the particle about the origin will be _______ kg m 2 s

JEE Main 2024 Solution View → 80

A cylinder is rolling down on an inclined plane of inclination 60 ° . Its acceleration during rolling down will be x 3 m s - 2 , where x = _______(use g = 10 m s - 2 ).

JEE Main 2024 Solution View → 81

A ring and a solid sphere roll down the same inclined plane without slipping. They start from rest. The radii of both bodies are identical and the ratio of their kinetic energies i

JEE Main 2024 Solution View → 82

A heavy iron bar of weight 12 kg is having its one end on the ground and the other on the shoulder of a man. The rod makes an angle 60 ° with the horizontal, the normal force appli

JEE Main 2024 Solution View → 83

Four particles, each of mass 1 kg are placed at four corners of a square of side 2 m . The moment of inertia of the system about an axis perpendicular to its plane and passing thro

JEE Main 2024 Solution View → 84

An annular disk of mass M , inner radius a and outer radius b is placed on a horizontal surface with coefficient of friction &#956; , as shown in the figure. At some time, an impul

JEE Advanced 2023 Solution View → 85

A thin circular coin of mass 5 gm and radius 4 3 cm is initially in a horizontal x y -plane. The coin is tossed vertically up ( + z direction) by applying an impulse of &#960; 2 &#

JEE Advanced 2023 Solution View → 86

A solid sphere and a solid cylinder of same mass and radius are rolling on a horizontal surface without slipping. The ratio of their radius of gyrations respectively k s p h : k c

JEE Main 2023 Solution View → 87

A light rope is wound around a hollow cylinder of mass 5 kg and radius 70 cm . The rope is pulled with a force of 52 . 5 N . The angular acceleration of the cylinder will be _____

JEE Main 2023 Solution View → 88

A solid sphere is rolling on a horizontal plane without slipping. If the ratio of angular momentum about axis of rotation of the sphere to the total energy of moving sphere is &#96

JEE Main 2023 Solution View → 89

For rolling spherical shell, the ratio of rotational kinetic energy and total kinetic energy is x 5 . The value of x is _____.

JEE Main 2023 Solution View → 90

A circular plate is rotating in horizontal plane, about an axis passing through its centre and perpendicular to the plate, with an angular velocity &#969; . A person sits at the ce

JEE Main 2023 Solution View → 91

A solid sphere of mass 500 g radius 5 cm is rotated about one of its diameter with angular speed of 10 rad s - 1 . If the moment of inertia of the sphere about its tangent is x &#2

JEE Main 2023 Solution View → 92

A force of - P k ^ acts on the origin of the coordinate system. The torque about the point ( 2 , - 3 ) is P ( a i ^ + b j ^ ) , The ratio of a b is x 2 . The value of x is

JEE Main 2023 Solution View → 93

The moment of inertia of a semicircular ring about an axis, passing through the center and perpendicular to the plane of ring, is 1 x MR 2 , where R is the radius and M is the mass

JEE Main 2023 Solution View → 94

A ring and a solid sphere rotating about an axis passing through their centres have same radii of gyration. The axis of rotation is perpendicular to plane of ring. The ratio of rad

JEE Main 2023 Solution View → 95

Two identical solid spheres each of mass 2 kg and radii 10 cm are fixed at the ends of a light rod. The separation between the centres of the spheres is 40 cm . The moment of inert

JEE Main 2023 Solution View → 96

Moment of inertia of a disc of mass M and radius &#39; R &#39; about any of its diameter is M R 2 4 . The moment of inertia of this disc about an axis normal to the disc and passin

JEE Main 2023 Solution View → 97

A solid cylinder is released from rest from the top of an inclined plane of inclination 30 &#176; and length 60 &#160; cm . If the cylinder rolls without slipping, its speed upon r

JEE Main 2023 Solution View → 98

Two discs of same mass and different radii are made of different materials such that their thicknesses are 1 cm and 0 . 5 cm respectively. The densities of materials are in the rat

JEE Main 2023 Solution View → 99

A solid sphere of mass 1 kg rolls without slipping on a plane surface. Its kinetic energy is 7 &#215; 10 - 3 J . The speed of the centre of mass of the sphere is ______ cm s - 1 .

JEE Main 2023 Solution View → 100

A uniform disc of mass 0 . 5 kg and radius r is projected with velocity 18 m s - 1 at t = 0 s on a rough horizontal surface. It starts off with a purely sliding motion at t = 0 s .

JEE Main 2023 Solution View → 101

A thin uniform rod of length 2 m , cross sectional area A and density d is rotated about an axis passing through the centre and perpendicular to its length with angular velocity &#

JEE Main 2023 Solution View → 102

A solid sphere of mass 2 kg is making pure rolling on a horizontal surface with kinetic energy 2240 J . The velocity of centre of mass of the sphere will be ______ m s - 1 .

JEE Main 2023 Solution View → 103

If a solid sphere of mass 5 kg and a disc of mass 4 kg have the same radius, then the ratio of moment of inertia of the disc about a tangent in its plane to the moment of inertia o

JEE Main 2023 Solution View → 104

An object of mass 8 kg is hanging from one end of a uniform rod C D of mass 2 kg and length 1 m pivoted at its end C on a vertical wall as shown in figure. It is supported by a cab

JEE Main 2023 Solution View → 105

I CM is moment of inertia of a circular disc about an axis (CM) passing through its center and perpendicular to the plane of disc. I AB is its moment of inertia about an axis AB pe

JEE Main 2023 Solution View → 106

A uniform solid cylinder with radius R and length L has moment of inertia I 1 , about the axis of cylinder. A concentric solid cylinder of radius R &#39; = R 2 and length L &#39; =

JEE Main 2023 Solution View → 107

Solid sphere A is rotating about an axis P Q . If the radius of the sphere is 5 cm , then its radius of gyration about P Q will be x cm . The value of x is _____.

JEE Main 2023 Solution View → 108

A flat surface of a thin uniform disk A of radius R is glued to a horizontal table. Another thin uniform disk B of mass M and with the same radius R rolls without slipping on the c

JEE Advanced 2022 Solution View → 109

At time t = 0 , a disk of radius 1 m starts to roll without slipping on a horizontal plane with an angular acceleration of &#945; = 2 3 rad s - 2 . A small stone is stuck to the di

JEE Advanced 2022 Solution View → 110

A solid sphere of mass 1 &#160; kg and radius 1 &#160; m rolls without slipping on a fixed inclined plane with an angle of inclination &#952; = 30 &#176; from the horizontal. Two f

JEE Advanced 2022 Solution View → 111

The torque of a force 5 i ^ + 3 j ^ - 7 k ^ about the origin is &#964; . If the force acts on a particle whose position vector is 2 i ^ + 2 j ^ + k ^ , then the value of &#964; wil

JEE Main 2022 Solution View → 112

Four identical discs each of mass &#39; M &#39; and diameter &#39; a &#39; are arranged in a small plane as shown in figure. If the moment of inertia of the system about O O &#39;

JEE Main 2022 Solution View → 113

A solid cylinder length is suspended symmetrically through two massless strings, as shown in the figure. The distance from the initial rest position, the cylinder should be unbindi

JEE Main 2022 Solution View → 114

A pulley of radius 1 . 5 m is rotated about its axis by a force F = 12 t - 3 t 2 N applied tangentially (while t is measured in seconds). If moment of inertia of the pulley about i

JEE Main 2022 Solution View → 115

The radius of gyration of a cylindrical rod about an axis of rotation perpendicular to its length and passing through the center will be _____ m . Given, the length of the rod is 1

JEE Main 2022 Solution View → 116

A disc of mass 1 kg and radius R is free of rotate about a horizontal axis passing through its centre and perpendicular to the plane of disc. A body of same mass as that of disc is

JEE Main 2022 Solution View → 117

A solid cylinder and a solid sphere, having same mass M and radius R , roll down the same inclined plane from top without slipping. They start from rest. The ratio of velocity of t

JEE Main 2022 Solution View → 118

The moment of inertia of a uniform thin rod about a perpendicular axis passing through one end is I 1 . The same rod is bent into a ring and its moment of inertia about a diameter

JEE Main 2022 Solution View → 119

A spherical shell of 1 kg mass and radius R is rolling with angular speed &#969; on horizontal plane (as shown in figure). The magnitude of angular momentum of the shell about the

JEE Main 2022 Solution View → 120

A 34 m long ladder weighing 10 kg leans on a frictionless wall. Its feet rest on the floor 3 m away from the wall as shown in the figure. If F f and F w are the reaction forces of

JEE Main 2022 Solution View →
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