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(C) The moment of inertia $I$ of a solid sphere of mass $M$ and radius $R$ about its diameter is given by $I = \frac{2}{5} M R^2$.Since the sphere has

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$\frac{176}{105} R^5 \rho$

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(C) The moment of inertia $I$ of a solid sphere of mass $M$ and radius $R$ about its diameter is given by $I = \frac{2}{5} M R^2$.Since the sphere has density $ho$,its mass $M$ is given by $M = 	ext{Volume} 	imes 	ext{density} = \left( \frac{4}{3} \pi R^3 ight) ho$.Substituting the value of $M$ into the formula for $I$:$I = \frac{2}{5} \left( \frac{4}{3} \pi R^3 ho ight) R^2$$I = \frac{8}{15} \pi R^5 ho$.Using $\pi \approx \frac{22}{7}$:$I = \frac{8}{15} 	imes \frac{22}{7} 	imes R^5 ho = \frac{176}{105} R^5 ho$.

The moment of inertia of a solid sphere of density $\rho$ and radius $R$ about its diameter is

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