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(C) The moment of inertia of a hollow sphere about its diameter is $I_{1} = \frac{2}{3} m r_{1}^{2}$.The moment of inertia of a solid sphere about its

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

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(C) The moment of inertia of a hollow sphere about its diameter is $I_{1} = \frac{2}{3} m r_{1}^{2}$.The moment of inertia of a solid sphere about its diameter is $I_{2} = \frac{2}{5} m r_{2}^{2}$.Given that the masses and moments of inertia are identical,we have $I_{1} = I_{2}$.Substituting the formulas: $\frac{2}{3} m r_{1}^{2} = \frac{2}{5} m r_{2}^{2}$.Canceling $2m$ from both sides,we get $\frac{r_{1}^{2}}{3} = \frac{r_{2}^{2}}{5}$.Rearranging the terms,$\frac{r_{1}^{2}}{r_{2}^{2}} = \frac{3}{5}$.Taking the square root of both sides,the ratio of their radii is $r_{1} : r_{2} = \sqrt{3} : \sqrt{5}$.

We have two spheres,one of which is hollow and the other 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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