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(B) Let the radii of the thin spherical shell and the solid sphere be $R_1$ and $R_2$,respectively.The moment of inertia of a thin spherical shell abo

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$\sqrt{3}: \sqrt{5}$

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(B) Let the radii of the thin spherical shell and the solid sphere be $R_1$ and $R_2$,respectively.The moment of inertia of a thin spherical shell about its diameter is given by:$I_{	ext{shell}} = \frac{2}{3} MR_1^2$ ... $(i)$The moment of inertia of a solid sphere about its diameter is given by:$I_{	ext{sphere}} = \frac{2}{5} MR_2^2$ ... (ii)Given that the masses $(M)$ and the moments of inertia $(I)$ for both bodies are equal,we equate $(i)$ and (ii):$\frac{2}{3} MR_1^2 = \frac{2}{5} MR_2^2$Dividing both sides by $M$ and simplifying:$\frac{R_1^2}{R_2^2} = \frac{3}{5}$Taking the square root on both sides:$\frac{R_1}{R_2} = \frac{\sqrt{3}}{\sqrt{5}}$Thus,the ratio of their radii is $\sqrt{3}: \sqrt{5}$.

Two spheres of equal masses,one of which is a thin spherical shell and the other a solid sphere,have the same moment of inertia about their respective diameters. The ratio of their radii is

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