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JEE Main 2023 (6 Apr, Shift 2) · Moment of Inertia & Radius of Gyration

Moment of Inertia & Radius of Gyration question from JEE Main 2023 (6 Apr, Shift 2)

Q98JEE Main 2023 · 6 APR · SHIFT 2Medium

Moment of Inertia & Radius of Gyration

A ring and a solid sphere rotating about an axis passing through their centers have same radii of gyration. The axis of rotation is perpendicular to plane of ring. The ratio of radius of ring to that of sphere is $\sqrt{\frac{2}{x}}$ . The value of $x$ is ___________.

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

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Answer: 5

Ring (perpendicular axis): $K^2 = R_r^2$ . Solid sphere: $K^2 = \frac{2}{5}R_s^2$ .
$R_r^2 = \frac{2}{5}R_s^2 \Rightarrow \frac{R_r}{R_s} = \sqrt{\frac{2}{5}}$
So $x = 5$ .

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