(D) When a body of mass $m$ and radius $R$ rolls down an inclined plane of height $h$ without slipping, its velocity at the bottom is given by $v = \s

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(D) When a body of mass $m$ and radius $R$ rolls down an inclined plane of height $h$ without slipping, its velocity at the bottom is given by $v = \sqrt{\frac{2gh}{1 + \frac{k^2}{R^2}}}$, where $k$ is the radius of gyration.For a ring, $k^2 = R^2$, so $v_R = \sqrt{\frac{2gh}{1+1}} = \sqrt{gh}$.For a solid disc, $k^2 = \frac{R^2}{2}$, so $v_D = \sqrt{\frac{2gh}{1+0.5}} = \sqrt{\frac{4gh}{3}} \approx 1.15 \sqrt{gh}$.For a solid sphere, $k^2 = \frac{2R^2}{5}$, so $v_S = \sqrt{\frac{2gh}{1+0.4}} = \sqrt{\frac{10gh}{7}} \approx 1.19 \sqrt{gh}$.Comparing the values, we find $V_S > V_D > V_R$.

Class 11 Physics System of Particles and Rotational Motion Rolling On Inclined Plane

Easy

Three bodies, a ring, a solid disc, and a solid sphere, roll down the same inclined plane without slipping. The radii of the bodies are identical, and they start from rest. If $V_S, V_R$, and $V_D$ are the speeds of the sphere, ring, and disc, respectively, when they reach the bottom, then the correct option is:

TS EAMCET 2019 All TS EAMCET

A
$V_S > V_R > V_D$
B
$V_D > V_S > V_R$
C
$V_R > V_D > V_S$
D
$V_S > V_D > V_R$

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System of Particles and Rotational Motion

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Rolling On Inclined Plane

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$A$ thin uniform,circular ring is rolling down an inclined plane of inclination $30^{\circ}$ without slipping. Its linear acceleration along the inclined plane will be

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$A$ solid sphere of mass $4 \ kg$ and radius $28 \ cm$ is on an inclined plane. If the acceleration of the sphere when it rolls down without sliding is $3.5 \ m \ s^{-2}$,then the acceleration of the sphere when it slides down without rolling is (in $m \ s^{-2}$)

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$A$ hollow cylinder of mass $m$ and radius $R$ is spinned to a clockwise angular velocity $\omega_0$ and then gently placed on an inclined plane for which the coefficient of friction is $\mu = \tan \theta$,where $\theta$ is the angle of the inclined plane with the horizontal. The centre of mass of the cylinder will remain stationary for time:

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$A$ solid sphere is rolling without slipping on a horizontal rough surface and starts rising on an inclined rough surface as shown in the figure. Assume pure rolling throughout the motion. Choose the $INCORRECT$ statement.

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