Question

The radius of gyration of a spherical shell of mass $M$ and radius $R$ about its tangential axis will be

• A. $\sqrt{\frac{2}{5}}R$
• B. $\sqrt{\frac{7}{5}}R$
• C. $\sqrt{\frac{2}{3}}R$
• D. $\sqrt{\frac{5}{3}}R$

Answer 1

The correct option is D $\sqrt{\frac{5}{3}}R$

Moment of inertia of the spherical shell about tangential axis is given by parallel axis theorem as
$I=I_{cm}+M{R}^2$
$\because I_{cm}=\frac{2}{3}M{R}^2$
$\therefore I=\frac{2}{3}M{R}^2+M{R}^2=\frac{5}{3}M{R}^2$
As $I=M{K}^2$
$\Rightarrow M{K}^2=\frac{5}{3}M{R}^2\Rightarrow K=\sqrt{\frac{5}{3}}R$