The radius of gyration K of a hollow sphere o | vedclass

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(A) The moment of inertia of a hollow sphere about an axis passing through its center is $I_{cm} = \frac{2}{3}MR^2$.By the parallel axis theorem, the

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$R/\sqrt{3}$

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(A) The moment of inertia of a hollow sphere about an axis passing through its center is $I_{cm} = \frac{2}{3}MR^2$.By the parallel axis theorem, the moment of inertia $I$ about an axis at a distance $h$ from the center is given by $I = I_{cm} + Mh^2$.Substituting the value of $I_{cm}$, we get $I = \frac{2}{3}MR^2 + Mh^2$.The radius of gyration $K$ is defined by the relation $I = MK^2$.Given that $K = R$, we have $I = MR^2$.Equating the two expressions for $I$:$MR^2 = \frac{2}{3}MR^2 + Mh^2$$R^2 = \frac{2}{3}R^2 + h^2$$h^2 = R^2 - \frac{2}{3}R^2$$h^2 = \frac{1}{3}R^2$$h = \frac{R}{\sqrt{3}}$Thus, the correct option is $A$.

The radius of gyration $K$ of a hollow sphere of mass $M$ and radius $R$ about an axis $XY$ is equal to $R$. The distance of that axis from the center of the sphere is $h$. The value of $h$ is

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