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JEE Main 2023 (25 Jan, Shift 2) · Moment of Inertia & Radius of Gyration

Moment of Inertia & Radius of Gyration question from JEE Main 2023 (25 Jan, Shift 2)

Q101JEE Main 2023 · 25 JAN · SHIFT 2Medium

Moment of Inertia & Radius of Gyration

If a solid sphere of mass 5 kg and a disc of mass 4 kg have the same radius. Then the ratio of moment of inertia of the disc about a tangent in its plane to the moment of inertia of the sphere about its tangent will be $\frac{x}{7}$ . The value of $x$ is ___________.

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

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Answer: 5

Disc about a tangent in its plane: $I_d = \frac{mR^2}{4} + mR^2 = \frac{5}{4}mR^2 = \frac{5}{4}(4)R^2 = 5R^2$ .
Sphere about a tangent: $I_s = \frac{2}{5}MR^2 + MR^2 = \frac{7}{5}(5)R^2 = 7R^2$ .
$\frac{I_d}{I_s} = \frac{5}{7}$ , so $x = 5$ .

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