Question

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

• 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

The correct option is C $\frac{176}{105}{R}^5\rho$

Moment of inertia of sphere about it diameter $I=\frac{2}{5}M{R}^2=\frac{2}{5}\left(\frac{4}{3}\pi R^3\rho \right)R^2$ $[AsM=V\rho =\frac{4}{3}\pi R^3\rho ]$
$l=\frac{8\pi }{15}{R}^5\rho =\frac{8\times 22}{15\times 7}{R}^5\rho =\frac{176}{105}{R}^5\rho$