Question

The moment of inertia of a solid sphere of mass $M$ and radius $R$ about a tangent to the sphere is

• A. $\frac{2}{5}M{R}^2$
• B. $\frac{6}{5}M{R}^2$
• C. $\frac{4}{5}M{R}^2$
• D. $\frac{7}{5}M{R}^2$

Answer 1

Answer: (D)

Moment of inertia of the solid sphere of mass $M$ and radius $R$ about any diameter is
$I_{\text{diameter}}=\frac{2}{5}M{R}^2$
According to theorem of parallel axes
$I_{\text{tangent}}=I_{\text{diameter}}+M{R}^2$
$=\frac{2}{5}M{R}^2+M{R}^2$
$=\frac{7}{5}M{R}^2$