What is the moment of inertia of a solid sphere of density $\rho$ and radius $\mathrm{R}$ about its diameter?

What is the moment of inertia of a solid sphere of density $\rho$ and radius $\mathrm{R}$ about its diameter?
  1. $\frac{105}{176} \mathrm{R}^{5} \rho$
  2. $\frac{105}{176} \mathrm{R}^{2} \rho$
  3. $\frac{176}{105} \mathrm{R}^{5} \rho$
  4. $\frac{176}{105} \mathrm{R}^{2} \rho$

Solution

For solid sphere $\begin{array}{l} I=\frac{2}{5} M R^{2}=\frac{2}{5}\left(\frac{4}{3} \pi R^{3} \rho\right) R^{2} \\ \rho=\frac{176}{105} R^{5} \rho \end{array}$ .

Asked in: MHT CET Full Test 12

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