The moment of inertia I of a solid sphere hav | vedclass

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(C) The volume of a solid sphere is given by $V = \frac{4}{3} \pi R^3$,where $R$ is the radius.From this,we have $R^3 \propto V$,which implies $R \pro

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$I \propto V^{5/3}$

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(C) The volume of a solid sphere is given by $V = \frac{4}{3} \pi R^3$,where $R$ is the radius.From this,we have $R^3 \propto V$,which implies $R \propto V^{1/3}$.The mass $M$ of the sphere is given by $M = 	ext{density} 	imes 	ext{Volume} = ho V$.The moment of inertia $I$ of a solid sphere about its diameter is $I = \frac{2}{5} M R^2$.Substituting $M = ho V$ and $R \propto V^{1/3}$ into the formula:$I = \frac{2}{5} (ho V) (V^{1/3})^2$$I = \frac{2}{5} ho V \cdot V^{2/3}$$I \propto V^{1 + 2/3}$$I \propto V^{5/3}$.

The moment of inertia $I$ of a solid sphere having fixed volume depends upon its volume $V$ as

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