Question

$K$ is radius of gyration of a circular ring about an axis in the plane of ring and at a perpendicular distance half of radius of ring from its centre. The radius of ring in terms of $K$ is:

• A. $\frac{K}{\sqrt{2}}$
• B. $\sqrt{2}K$
• C. $\frac{2K}{\sqrt{3}}$
• D. $\frac{\sqrt{3}K}{2}$

Answer 1

The correct option is C $\frac{2K}{\sqrt{3}}$

Moment of inertia of ring about an axis in the plane $I_{cm}=M{R}^2/2$

Now using parallel axis theorem $I=I_{cm}+M{d}^2$ where $d=\frac{R}{2}$

$I=M{R}^2/2+M{R}^2/4=\frac{3M{R}^2}{4}$

So $I=M{K}^2=\frac{3M{R}^2}{4}$

We get $K=\frac{R\sqrt{3}}{2}$ , $R=\frac{2K}{\sqrt{3}}$