A solid sphere and a thin-walled hollow spher | vedclass

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(C) The moment of inertia of a solid sphere about its diameter is given by $I_{s} = \frac{2}{5}MR^{2}$.The moment of inertia of a thin-walled hollow s

Vedclass · Accepted Answer

$I_{h} > I_{s}$

Vedclass · Answer

(C) The moment of inertia of a solid sphere about its diameter is given by $I_{s} = \frac{2}{5}MR^{2}$.The moment of inertia of a thin-walled hollow sphere about its diameter is given by $I_{h} = \frac{2}{3}MR^{2}$.Since both spheres have the same mass $M$ and the same material,they must have the same volume if they were the same size,but for a solid and hollow sphere of the same mass,the radius $R$ of the hollow sphere must be larger than the radius of the solid sphere to maintain the same mass density distribution.Even if we assume the radii are the same,comparing the coefficients: $\frac{2}{3} \approx 0.667$ and $\frac{2}{5} = 0.4$.Since $0.667 > 0.4$,it follows that $I_{h} > I_{s}$.

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