Question

What is the moment of inertia of 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)

Moment of inertia of solid sphere of mass $M$, density $\rho$ and radius $R$ about its diameter is
$I=\frac{2}{5}MR^{2}=\frac{2}{5}\left(\frac{4}{3}\pi R^{3}\rho\right)R^{2}$
$=\frac{8}{15}\pi R^{5}\rho=\frac{8}{15}\times\frac{22}{7}\pi R^{5}\rho$
$=\frac{176}{105}R^{5}\rho$