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(C) Let the mass of both spheres be $m$. Let the radius of the solid sphere be $r_1$ and the radius of the hollow sphere be $r_2$.The moment of inerti

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

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(C) Let the mass of both spheres be $m$. Let the radius of the solid sphere be $r_1$ and the radius of the hollow sphere be $r_2$.The moment of inertia of a solid sphere about its diameter is $I_1 = \frac{2}{5} m r_1^2$.The moment of inertia of a hollow sphere about its diameter is $I_2 = \frac{2}{3} m r_2^2$.Given that the moments of inertia are identical $(I_1 = I_2)$,we have:$\frac{2}{5} m r_1^2 = \frac{2}{3} m r_2^2$Canceling $2m$ from both sides:$\frac{r_1^2}{5} = \frac{r_2^2}{3}$Rearranging to find the ratio of the radii $(r_1 : r_2)$:$\frac{r_1^2}{r_2^2} = \frac{5}{3}$Taking the square root of both sides:$\frac{r_1}{r_2} = \sqrt{\frac{5}{3}} = \frac{\sqrt{5}}{\sqrt{3}}$Thus,the ratio of their radii is $\sqrt{5} : \sqrt{3}$.

We have two spheres,one of which is a hollow shell and the other is solid. They have identical masses and moments of inertia about their respective diameters. The ratio of their radii is given by

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