Question

The radius of a solid sphere is R and its density D. When it is made to rotate about an axis passing through any diameter of sphere, expression for its moment of inertia is

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

Density of the solid sphere, $\rho =D$

$\therefore$ Moment of inertia $\left(I\right)=\frac{2}{5}M{R}^2$

$\Rightarrow I=\frac{2}{5}\left(\rho V\right)R^2$

$=\frac{2}{5}\left(D\right)\left(\frac{4}{3}\pi R^3\right)\left(R^2\right)$

$I=\frac{8}{15}\pi D{R}^5$