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(C) Let $M$ be the mass of both spheres. Let $R_1$ be the radius of the hollow sphere and $R_2$ be the radius of the solid sphere.The moment of inerti

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

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(C) Let $M$ be the mass of both spheres. Let $R_1$ be the radius of the hollow sphere and $R_2$ be the radius of the solid sphere.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 moments of inertia are identical $(I_1 = I_2)$,we have:$\frac{2}{3} M R_1^2 = \frac{2}{5} M R_2^2$Canceling $M$ and the factor of $2$ from both sides:$\frac{R_1^2}{3} = \frac{R_2^2}{5}$Rearranging to find the ratio of the radii:$\frac{R_1^2}{R_2^2} = \frac{3}{5}$Taking the square root of both sides:$\frac{R_1}{R_2} = \sqrt{\frac{3}{5}} = \frac{\sqrt{3}}{\sqrt{5}}$Thus,the ratio is $\sqrt{3} : \sqrt{5}$.

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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