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)

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

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