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
$I=\frac{2}{5}M{R}^2=\frac{2}{5}\left(\frac{4}{3}\pi R^3\rho \right)R^2$
$=\frac{8}{15}\pi R^5\rho =\frac{8}{15}\times \frac{22}{7}\pi R^5\rho$
$=\frac{176}{105}{R}^5\rho$