Question

The moment of inertia of a sphere of mass $M$ and radius $R$ about an axis passing through its centre is $\frac{2}{5}M{R}^2$. The radius of gyration of the sphere about a parallel axis tangent to the sphere is :

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

Answer 1

The correct option is C $\frac{\sqrt{7}}{\sqrt{5}}R$

$I_{tangent}=\frac{2}{5}M{R}^2+M{R}^2$$=\frac{7}{5}M{R}^2$
Radius of gyration is equivalent lenght at which whole mass can be considered to be concentrated so forming the equation as,
$\Rightarrow \frac{7}{5}M{R}^2=M{K}^2$

$\Rightarrow K=\sqrt{\frac{7}{5}}R$