Question

The mass of a circular ring is $M$ and its radius is $R$. Find its moment of inertia is about an axis in the plane of ring at a perpendicular distance $\frac{R}{2}$ from the centre of ring.

• A. $\frac{M{R}^2}{4}$
• B. $\frac{M{R}^2}{2}$
• C. $\frac{3M{R}^2}{2}$
• D. $\frac{3M{R}^2}{4}$

Answer 1

The correct option is D $\frac{3M{R}^2}{4}$

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

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

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