Question

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

• A. $\frac{105}{176} R^{5}\rho$
• B. $\frac{105}{176} R^{2}\rho$
• C. $\frac{176}{105} R^{5}\rho$
• D. $\frac{176}{105} R^{2}\rho$

Answer 1

Answer: (C)

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

Answer 2

For solid sphere
$I = \frac{2}{5} MR^{2} = \frac{2}{5} \left(\frac{4}{3}\pi R^{3} \rho\right)R^{2}$
$\rho = \frac{176}{105} R^{5} \rho$