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JEE Main 2025 (4 Apr, Shift 1) · Rolling Motion

Rolling Motion question from JEE Main 2025 (4 Apr, Shift 1)

Q18JEE Main 2025 · 4 APR · SHIFT 1Medium

Rolling Motion

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 $x =$ ________.

Numerical answer type. Work it out, then open the answer.

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Answer: 4

Rolling from height $h$ : $v^2 = \dfrac{2gh}{1 + k^2/R^2}$ .
Ring: $v_r^2 = gh$ ; solid sphere: $v_s^2 = \frac{10}{7}gh$ .
$\dfrac{v_r}{v_s} = \sqrt{\dfrac{7}{10}} = \sqrt{\dfrac{3.5}{5}}$ , so $x = 3.5$ .

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