We have two spheres,one of which is a hollow | vedclass

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(C) Let the mass of both spheres be $m$. Let $r_1$ be the radius of the solid sphere and $r_2$ be the radius of the hollow sphere.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 $r_1$ be the radius of the solid sphere and $r_2$ be the radius of the hollow sphere.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 (shell) about its diameter is $I_2 = \frac{2}{3} m r_2^2$.Given that the moments of inertia are identical,$I_1 = I_2$.Therefore,$\frac{2}{5} m r_1^2 = \frac{2}{3} m r_2^2$.Simplifying the equation,we get $\frac{r_1^2}{5} = \frac{r_2^2}{3}$.Rearranging for the ratio of radii,$\frac{r_1^2}{r_2^2} = \frac{5}{3}$.Taking the square root on both sides,$\frac{r_1}{r_2} = \sqrt{\frac{5}{3}} = \sqrt{5} : \sqrt{3}$.

We have two spheres,one of which is a hollow shell 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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