Rotational Dynamics | JEE Main previous year questions with Solutions

Q 1 :

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 $\frac{x}{5}$ . The value of $x$ is _______ . [2024]

(2) $\frac{K E_{Rot}}{K E_{Trans}} = \frac{\frac{1}{2} I ω^{2}}{\frac{1}{2} I ω^{2} + \frac{1}{2} m v^{2}} = \frac{(\frac{1}{2}) (\frac{2}{3} m R^{2}) ω^{2}}{(\frac{1}{2}) (\frac{2}{3} m R^{2}) ω^{2} + \frac{1}{2} m {(R ω)}^{2}}$

$\Rightarrow \frac{K E_{Rot}}{K E_{Trans}} = \frac{\frac{2}{3}}{\frac{2}{3} + 1} = \frac{2}{5}$

Hence, $x = 2$

Q 2 :

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 ${(\frac{α}{2})}^{1 / 2}$ $t$ $s$ , where $α$ is _______ . [2024]

(3) If disc slips on inclined plane, then it's acceleration, $a_{1} = g \sin θ$

$l = \frac{1}{2} a_{1} t_{1}^{2} \Rightarrow t = \sqrt{\frac{2 l}{g \sin θ}}$ $\dots (i)$

If disc rolls on inclined plane its acceleration,

$a_{2} = \frac{g \sin θ}{1 + \frac{I}{m R^{2}}} = \frac{g \sin θ}{1 + \frac{m R^{2}}{2 m R^{2}}} = \frac{2}{3} g \sin θ$

Now $l = \frac{1}{2} a_{2} t_{2}^{2} \Rightarrow t_{2} = \sqrt{\frac{2 l}{\frac{2}{3} g \sin θ}}$

$\Rightarrow t_{2} = \sqrt{\frac{3}{2}} \sqrt{\frac{2 l}{g \sin θ}} = \sqrt{\frac{3}{2}} t$ $\dots (i i)$

On comparing, $\sqrt{\frac{3}{2}} t = \sqrt{\frac{α}{2}} t \Rightarrow α = 3$

Q 3 :

A solid sphere and a hollow cylinder roll up without slipping on the same inclined plane with the same initial speed v. The sphere and the cylinder reach up to maximum heights $h_{1}$ and $h_{2}$ , respectively, above the initial level. The ratio $h_{1} : h_{2}$ is $\frac{n}{10}$ . The value of n is _____. [2024]

(7)

Energy conservation, Gain in P.E. = Loss in K.E.

$\frac{1}{2} m v^{2} + \frac{1}{2} I ω^{2} = m g h$

For pure rolling; $v = ω R$

$\frac{1}{2} m v^{2} + \frac{1}{2} I \frac{v^{2}}{R^{2}} = m g h$

$\frac{1}{2} v^{2} (m + \frac{m K^{2}}{R^{2}}) = m g h$

$\Rightarrow m g h = \frac{1}{2} m v^{2} (1 + \frac{K^{2}}{R^{2}}) \Rightarrow h \propto 1 + \frac{K^{2}}{R^{2}}$

$\frac{h_{1}}{h_{2}} = \frac{1 + \frac{2}{5}}{1 + 1} = \frac{7}{5 \times 2} = \frac{7}{10}$

Hence, $n = 7$

Q 4 :

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 horizontal. The speed of the particle at the bottom of the plane is $v_{1}$ . If the angle of inclination is increased to 45° while keeping L constant. Then the new speed of the sphere at the bottom of the plane is $v_{2}$ . The ratio of $v_{1}^{2} : v_{2}^{2}$ is [2025]

$1 : \sqrt{2}$
1 : 3
1 : 2
$1 : \sqrt{3}$

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(1)

Loss in P.E. = gain in K.E.

$m g L \sin θ = \frac{1}{2} (\frac{7}{5}) m v^{2} \Rightarrow v^{2} \propto \sin θ$

$\Rightarrow \frac{v_{1}^{2}}{v_{2}^{2}} = \frac{\sin 30 °}{\sin 45 °} = \frac{1}{\sqrt{2}}$

Q 5 :

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 linear acceleration of the cylinder axis will be: [2025]

$\frac{1}{\sqrt{2}} g$
$\frac{1}{3 \sqrt{2}} g$
$\frac{\sqrt{2} g}{3}$
$\sqrt{2} g$

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(3)

$a = \frac{g \sin θ}{1 + \frac{I}{m r^{2}}}$

$a = \frac{\frac{g}{\sqrt{2}}}{1 + \frac{1}{2}} = \frac{2 \frac{g}{\sqrt{2}}}{3} = \frac{\sqrt{2} g}{3}$

Q 6 :

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 sphere be $t_{1}$ and $t_{2}$ , respectively, then [2025]

$t_{1} < t_{2}$
$t_{1} = t_{2}$
$t_{1} = 2 t_{2}$
$t_{1} > t_{2}$

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(1)

The time taken to reach the bottom, $t = \sqrt{\frac{2 l}{a_{cm}}}$

Acceleration, $a_{cm} = \frac{g \sin θ}{1 + \frac{I_{cm}}{M R^{2}}}$

$a_{1} = a_{{cm}_{1}} = \frac{5 g \sin θ}{7}$ ... Solid

$a_{2} = a_{{cm}_{2}} = \frac{3 g \sin θ}{5}$ ... Hollow

As $a_{1} > a_{2}$ hence, $t_{1} < t_{2}$

Q 7 :

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 acceleration of the center of the sphere is [2025]

3.5 $m / s^{2}$
0.35 $m / s^{2}$
2.5 $m / s^{2}$
0.25 $m / s^{2}$

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(1)

Torque about bottom point, $F \times 2 r = I α$

$49 \times 2 r = \frac{7}{5} m r^{2} α$

$14 = 4 r α$ ... (i)

As sphere rolls without slipping

$a = r α$ ... (ii)

$\Rightarrow a = \frac{14}{4} = \frac{7}{2} = 3.5 m / s^{2}$

Q 8 :

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 plane is $\sqrt{\frac{x}{5}}$ where x = __________. [2025]

(4)

Applying Mechanical Energy conservation:

$k_{i} + U_{i} = k_{f} + U_{f}$

$\Rightarrow 0 + m g h = \frac{1}{2} m v^{2} (1 + \frac{k^{2}}{R^{2}}) + 0$

$\Rightarrow V = \sqrt{\frac{2 g h}{1 + \frac{k^{2}}{R^{2}}}}$

So, Ratio of velocities

$\frac{V_{Ring}}{V_{Solid sphere}} = \sqrt{\frac{1 + \frac{2}{5}}{1 + 1}} = \sqrt{\frac{7}{10}}$

x = 3.5 $\Rightarrow$ Rounding off x = 4.

Q 9 :

A disc is rolling without slipping on a surface. The radius of the disc is R. At $t = 0$ , the top most point on the disc is A, as shown in the figure. When the disc completes half of its rotation, the displacement of point A from its initial position is [2023]

$R \sqrt{(π^{2} + 4)}$
$R \sqrt{(π^{2} + 1)}$
$2 R$
$2 R \sqrt{(1 + 4 π^{2})}$

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(1)

$Displacement = \sqrt{{(2 R)}^{2} + (π R^{2})} = R \sqrt{4 + π^{2}}$

Q 10 :

A solid cylinder is released from rest from the top of an inclined plane of inclination 30° and length 60 cm. If the cylinder rolls without slipping, its speed upon reaching the bottom of the inclined plane is ________ ${ms}^{- 1}$ . (Given g = 10 ${ms}^{- 2}$ ) [2023]

(2)

$v = \sqrt{\frac{2 g h}{1 + \frac{k^{2}}{R^{2}}}}$

$Where h = 60 \sin 30 ° = 30 cm$

$and k^{2} = \frac{R^{2}}{2}$

$\Rightarrow v = 2 {ms}^{- 1}$

Q 11 :

A hollow spherical ball of uniform density rolls up a curved surface with an initial velocity 3 m/s (as shown in figure). Maximum height with respect to the initial position covered by it will be ________ cm (take g = 10 $m / s^{2}$ ) [2023]

(75)

$At highest point K E_{f} = 0$

$Initial K E = Translational KE + Rotational KE$

$= \frac{1}{2} m v^{2} + \frac{1}{2} I ω^{2}$

$In case of rolling v = R ω$

$= \frac{1}{2} m v^{2} + \frac{1}{2} \times \frac{2}{3} m R^{2} \times \frac{v^{2}}{R^{2}} = \frac{5}{6} m v^{2}$

$Apply energy conservation, K E_{i} + P E_{i} = K E_{f} + P E_{f}$

$\frac{5}{6} m v^{2} = m g h$

$h = \frac{5}{6 \times 10} \times 9 m = \frac{15}{20} m = 75 cm$

Q 12 :

For a rolling spherical shell, the ratio of rotational kinetic energy and total kinetic energy is $\frac{x}{5}$ . The value of $x$ is ________. [2023]

(2)

$\frac{K_{rot}}{K_{total}} = \frac{\frac{1}{2} (\frac{2}{3} m R^{2}) {(\frac{v}{R})}^{2}}{\frac{1}{2} m v^{2} + \frac{1}{2} (\frac{2}{3} m R^{2}) {(\frac{v}{R})}^{2}}$

$\Rightarrow \frac{x}{5} = \frac{2}{5} \Rightarrow x = 2$

Q 13 :

A solid sphere is rolling on a horizontal plane without slipping. If the ratio of angular momentum about the axis of rotation of the sphere to the total energy of the moving sphere is $π : 22$ , then the value of its angular speed will be ________ rad/s. [2023]

(4)

$L = (I_{com}) (ω) and K = \frac{1}{2} (I_{com}) (ω^{2}) + \frac{1}{2} M V_{com}^{2}$

$L = \frac{2}{5} M R^{2} \frac{V_{com}}{R}$

$K = \frac{1}{2} (\frac{2}{5} M R^{2}) \frac{v_{com}^{2}}{R^{2}} + \frac{1}{2} M V_{com}^{2}$

$L = \frac{2 M R V_{com}}{5} K = \frac{7}{10} M V_{com}^{2}$

$Ratio \frac{L}{K} = \frac{4}{7} \frac{R}{v_{com}} = \frac{π}{22} \Rightarrow ω = \frac{4}{7} \times \frac{22}{22} \times 7 = 4$

Q 14 :

A thin uniform rod $(X)$ of mass $M$ and length $L$ is pivoted at a height $(\frac{L}{3})$ as shown in the figure. The rod is allowed to fall from a vertical position and lie horizontally on the table. The angular velocity of this rod when it hits the table top is __________.

(g = gravitational acceleration) [2026]

$\sqrt{\frac{3}{2} \frac{g}{L}}$
$\frac{3}{\sqrt{2}} \sqrt{\frac{g}{L}}$
$\frac{1}{\sqrt{2}} \sqrt{\frac{g}{L}}$
$\sqrt{\frac{3 g}{L}}$

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(4)

$m g \frac{ℓ}{6} = \frac{1}{2} I ω^{2}$

$Here I = \frac{m ℓ^{2}}{12} + \frac{m ℓ^{2}}{36} = \frac{m ℓ^{2}}{9}$

$m g \frac{ℓ}{6} = \frac{m ℓ^{2}}{18} ω^{2} \Rightarrow ω^{2} = \frac{3 g}{ℓ}$

$ω = \sqrt{\frac{3 g}{ℓ}}$

Q 15 :

A tennis ball (treated as hollow spherical shell) starting from O rolls down a hill. At point A the ball becomes air borne leaving at an angle of $30 °$ with the horizontal. The ball strikes the ground at B. What is the value of the distance AB? (Moment of inertia of a spherical shell of mass $m$ and radius $R$ about its diameter = $\frac{2}{3} m R^{2}$ )

1.87 m
2.08 m
1.57 m
1.77 m

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(1)

Velocity of the tennis ball on the surface the earth or ground

$v = \sqrt{\frac{2 g h}{1 + \frac{k^{2}}{R^{2}}}}$ (where $k =$ radius of gyration of spherical shell $= \sqrt{\frac{2}{3}} R$

Horizontal range AB $= \frac{v^{2} \sin 2 θ}{g}$ $= \frac{{(\sqrt{\frac{2 g h}{1 + \frac{k^{2}}{R^{2}}}})}^{2} \sin (2 \times 30 °)}{g} = 1.87 m$

Q 16 :

When a body is under pure rolling, the fraction of its total kinetic energy which is purely rotational is $\frac{2}{5}$ . Identify the body.

Hollow sphere
Sphere
Ring
Disc

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(1)

$\frac{Rotational K.E.}{Total K.E.} = \frac{2}{5}$

$\Rightarrow \frac{\frac{1}{2} I ω^{2}}{\frac{1}{2} m v^{2} + \frac{1}{2} I ω^{2}} = \frac{2}{5}$

$\Rightarrow \frac{\frac{1}{2} m K^{2} ω^{2}}{\frac{1}{2} m R^{2} ω^{2} + \frac{1}{2} m K^{2} ω^{2}} = \frac{2}{5}$

$\Rightarrow \frac{K^{2}}{K^{2} + R^{2}} = \frac{2}{5}$

$\Rightarrow K^{2} = \frac{2}{3} R^{2}$ $or$ $K = \sqrt{\frac{2}{3}} R$

$So it will be hollow sphere.$

Q 17 :

STATEMENT-1: Two cylinders, one hollow (metal) and the other solid (wood) with the same mass and identical dimensions are simultaneously allowed to roll without slipping down an inclined plane from the same height. The hollow cylinder will reach the bottom of the inclined plane first.

and

STATEMENT-2: By the principle of conservation of energy, the total kinetic energies of both the cylinders are identical when they reach the bottom of the incline.

Statement-1 is True, Statement-2 is True; Statement-2 is a correct explanation for Statement-1
Statement-1 is True, Statement-2 is True; Statement-2 is NOT a correct explanation for Statement-1
Statement-1 is True, Statement-2 is False
Statement-1 is False, Statement-2 is True

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(4)

$By conservation of energy, we have \frac{1}{2} m v_{c}^{2} + \frac{1}{2} I_{c} ω^{2} = m g h$

$Moment of inertia of solid and hollow cylinders are given as I_{solid} = \frac{M R^{2}}{2}, I_{hollow} = M R^{2}$

$For pure rolling, we have ω = \frac{v_{c}}{R}, As I_{solid} < I_{hollow} \Rightarrow v_{solid} > v_{hollow}$

$Hence solid cylinder will reach the bottom first.$

Q 18 :

Assertion: Rolling without slipping cannot possible in absence of friction.

Reason: During rolling without slipping, energy can remain conserved in absence of external applied force.

Assertion is True, Reason is True, Reason is correct explanation for Assertion
Assertion is True, Reason is True, Reason is NOT a correct explanation for Assertion
Assertion is True, Reason is false
Assertion is False, Reason is True

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(4)

In uniform pure rolling, the linear velocity is constant. If no external force or torque is applied, the body will remain in a state of uniform pure rolling. In this case, the friction force is always zero, so there will not be any effect of the frictional force on the body.

Q 19 :

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 $v_{0} = 49$ m/s, perpendicular to its axis and a rotational velocity $v_{0} / 4 R$ about the centre. The time taken by the cylinder to start rolling is ______ seconds. (coefficient of kinetic friction $μ_{K}$ = 0.25 and g = 9.8 ${m/s}^{2}$ ) [2026]

15
5
10
7.5

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(2)

$\vec{L} is conserved about A :$

$M v_{0} R + \frac{M R^{2}}{2} ω = M v R + \frac{M R^{2}}{2} ω$

$M v_{0} R + \frac{M R^{2}}{2} (\frac{v_{0}}{4 R}) = M v R + \frac{M R^{2}}{2} (\frac{v}{R})$

$M v_{0} R + \frac{M v_{0} R}{8} = M v R + \frac{M v R}{2}$

$\frac{9 M v_{0} R}{8} = \frac{3 M v R}{2} \Rightarrow v = \frac{3 v_{0}}{4}$

$v = v_{0} + a t$

$\frac{3 v_{0}}{4} = v_{0} - μ_{k} g t$

$μ_{k} g t = \frac{v_{0}}{4} \Rightarrow t = \frac{v_{0}}{4 μ_{k} g}$

$\Rightarrow t = \frac{v_{0}}{4 μ_{k} g} = \frac{49}{4 \times \frac{1}{4} \times 9.8} = 5 \sec$

Q 20 :

An object of uniform density rolls up the curved path with the initial velocity $v_{0}$ as shown in the figure. If the maximum height attained by an object is $\frac{7 v_{0}^{2}}{10 g}$ ( $g =$ acceleration due to gravity), the object is a _______. [2026]

solid cylinder
ring
disc
solid sphere

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(4)

$Applying COME,$

$\Rightarrow m g (\frac{7 v_{0}^{2}}{10 g}) = (1 + \frac{K^{2}}{R^{2}}) \frac{1}{2} m v_{0}^{2}$

Q 21 :

A solid sphere (A) of mass 5m and spherical shell (B) of mass m, both having same radius, are placed on a rough surface. When a force of same magnitude is applied tangentially at the highest points of A and B, they start rolling without slipping with an acceleration of $a_{A}$ and $a_{B}$ , respectively. The ratio of $a_{A}$ and $a_{B}$ is ________. [2026]

5 : 21
6 : 10
21 : 25
1 : 5

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(1)

$τ_{p} = I_{p} α \Rightarrow F (2 R) = I \frac{a}{R}$

$a = \frac{2 F R^{2}}{I} \Rightarrow \frac{a_{A}}{a_{B}} = \frac{I_{B}}{I_{A}}$

$Solid sphere (A) : I_{A} = \frac{2}{5} (5 m) R^{2} + (5 m) R^{2} = 7 m R^{2}$

$Spherical shell (B) : I_{B} = \frac{2}{3} m R^{2} + m R^{2} = \frac{5}{3} m R^{2}$

$\frac{a_{A}}{a_{B}} = \frac{I_{B}}{I_{A}} = \frac{\frac{5}{3} m R^{2}}{7 m R^{2}} = \frac{5}{21}$

Topic Question Set

Q 1 :

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 $\frac{x}{5}$ . The value of $x$ is _______ . [2024]

Q 2 :

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 ${(\frac{α}{2})}^{1 / 2}$ $t$ $s$ , where $α$ is _______ . [2024]

Q 5 :

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 linear acceleration of the cylinder axis will be: [2025]

Q 6 :

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 sphere be $t_{1}$ and $t_{2}$ , respectively, then [2025]

Q 7 :

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 acceleration of the center of the sphere is [2025]

Q 8 :

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 plane is $\sqrt{\frac{x}{5}}$ where x = __________. [2025]

Q 9 :

A disc is rolling without slipping on a surface. The radius of the disc is R. At $t = 0$ , the top most point on the disc is A, as shown in the figure. When the disc completes half of its rotation, the displacement of point A from its initial position is [2023]

Q 10 :

A solid cylinder is released from rest from the top of an inclined plane of inclination 30° and length 60 cm. If the cylinder rolls without slipping, its speed upon reaching the bottom of the inclined plane is ________ ${ms}^{- 1}$ . (Given g = 10 ${ms}^{- 2}$ ) [2023]

Q 11 :

A hollow spherical ball of uniform density rolls up a curved surface with an initial velocity 3 m/s (as shown in figure). Maximum height with respect to the initial position covered by it will be ________ cm (take g = 10 $m / s^{2}$ ) [2023]

Q 12 :

For a rolling spherical shell, the ratio of rotational kinetic energy and total kinetic energy is $\frac{x}{5}$ . The value of $x$ is ________. [2023]

Q 13 :

A solid sphere is rolling on a horizontal plane without slipping. If the ratio of angular momentum about the axis of rotation of the sphere to the total energy of the moving sphere is $π : 22$ , then the value of its angular speed will be ________ rad/s. [2023]

Q 16 :

When a body is under pure rolling, the fraction of its total kinetic energy which is purely rotational is $\frac{2}{5}$ . Identify the body.

Q 18 :

Assertion: Rolling without slipping cannot possible in absence of friction.

Reason: During rolling without slipping, energy can remain conserved in absence of external applied force.

Q 20 :

An object of uniform density rolls up the curved path with the initial velocity $v_{0}$ as shown in the figure. If the maximum height attained by an object is $\frac{7 v_{0}^{2}}{10 g}$ ( $g =$ acceleration due to gravity), the object is a _______. [2026]

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Topic Question Set

Q 1 : 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 x5. The value of x is _______ . [2024]

Q 2 : 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 (α2)1/2 t s, where α is _______ . [2024]

Q 3 : A solid sphere and a hollow cylinder roll up without slipping on the same inclined plane with the same initial speed v. The sphere and the cylinder reach up to maximum heights h1 and h2, respectively, above the initial level. The ratio h1:h2 is n10. The value of n is _____. [2024]

Q 5 : 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 linear acceleration of the cylinder axis will be: [2025]

Q 6 : 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 sphere be t1 and t2, respectively, then [2025]

Q 7 : 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 acceleration of the center of the sphere is [2025]

Q 8 : 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 plane is x5 where x = __________. [2025]

Q 9 : A disc is rolling without slipping on a surface. The radius of the disc is R. At t=0, the top most point on the disc is A, as shown in the figure. When the disc completes half of its rotation, the displacement of point A from its initial position is [2023]

Q 10 : A solid cylinder is released from rest from the top of an inclined plane of inclination 30° and length 60 cm. If the cylinder rolls without slipping, its speed upon reaching the bottom of the inclined plane is ________ ms-1. (Given g = 10 ms-2) [2023]

Q 11 : A hollow spherical ball of uniform density rolls up a curved surface with an initial velocity 3 m/s (as shown in figure). Maximum height with respect to the initial position covered by it will be ________ cm (take g = 10 m/s2) [2023]

Q 12 : For a rolling spherical shell, the ratio of rotational kinetic energy and total kinetic energy is x5. The value of x is ________. [2023]

Q 13 : A solid sphere is rolling on a horizontal plane without slipping. If the ratio of angular momentum about the axis of rotation of the sphere to the total energy of the moving sphere is π:22, then the value of its angular speed will be ________ rad/s. [2023]

Q 16 : When a body is under pure rolling, the fraction of its total kinetic energy which is purely rotational is 25. Identify the body.

Q 18 : Assertion: Rolling without slipping cannot possible in absence of friction. Reason: During rolling without slipping, energy can remain conserved in absence of external applied force.

Q 20 : 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 7v0210g (g= acceleration due to gravity), the object is a _______. [2026]

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Q 1 :

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 $\frac{x}{5}$ . The value of $x$ is _______ . [2024]

Q 2 :

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 ${(\frac{α}{2})}^{1 / 2}$ $t$ $s$ , where $α$ is _______ . [2024]

Q 5 :

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 linear acceleration of the cylinder axis will be: [2025]

Q 6 :

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 sphere be $t_{1}$ and $t_{2}$ , respectively, then [2025]

Q 7 :

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 acceleration of the center of the sphere is [2025]

Q 8 :

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 plane is $\sqrt{\frac{x}{5}}$ where x = __________. [2025]

Q 9 :

A disc is rolling without slipping on a surface. The radius of the disc is R. At $t = 0$ , the top most point on the disc is A, as shown in the figure. When the disc completes half of its rotation, the displacement of point A from its initial position is [2023]

Q 10 :

A solid cylinder is released from rest from the top of an inclined plane of inclination 30° and length 60 cm. If the cylinder rolls without slipping, its speed upon reaching the bottom of the inclined plane is ________ ${ms}^{- 1}$ . (Given g = 10 ${ms}^{- 2}$ ) [2023]

Q 11 :

A hollow spherical ball of uniform density rolls up a curved surface with an initial velocity 3 m/s (as shown in figure). Maximum height with respect to the initial position covered by it will be ________ cm (take g = 10 $m / s^{2}$ ) [2023]

Q 12 :

For a rolling spherical shell, the ratio of rotational kinetic energy and total kinetic energy is $\frac{x}{5}$ . The value of $x$ is ________. [2023]

Q 13 :

A solid sphere is rolling on a horizontal plane without slipping. If the ratio of angular momentum about the axis of rotation of the sphere to the total energy of the moving sphere is $π : 22$ , then the value of its angular speed will be ________ rad/s. [2023]

Q 16 :

When a body is under pure rolling, the fraction of its total kinetic energy which is purely rotational is $\frac{2}{5}$ . Identify the body.

Q 18 :

Assertion: Rolling without slipping cannot possible in absence of friction.

Reason: During rolling without slipping, energy can remain conserved in absence of external applied force.

Q 20 :

An object of uniform density rolls up the curved path with the initial velocity $v_{0}$ as shown in the figure. If the maximum height attained by an object is $\frac{7 v_{0}^{2}}{10 g}$ ( $g =$ acceleration due to gravity), the object is a _______. [2026]