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JEE Main 2022 (25 Jul, Shift 1) · Rolling Motion

Rolling Motion question from JEE Main 2022 (25 Jul, Shift 1)

Q49JEE Main 2022 · 25 JUL · SHIFT 1Medium

Rolling Motion

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 the solid cylinder to that of the solid sphere, with which they reach the ground, will be:

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Answer: (d)

Rolling from height $h$ : $v^2 = \dfrac{2gh}{1 + k^2/R^2}$ .
Cylinder: $v_c^2 = \frac{4}{3}gh$ ; sphere: $v_s^2 = \frac{10}{7}gh$ .
$\dfrac{v_c}{v_s} = \sqrt{\dfrac{4/3}{10/7}} = \sqrt{\dfrac{14}{15}}$
So the answer is (d).

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