Question

$M$ is mass and $R$ is radius of a circular ring. The moment of inertia of same ring about an axis in the plane of ring at a perpendicular distance $\frac{2R}{3}$ from centre of ring is:

• A. $\frac{2M{R}^2}{3}$
• B. $\frac{4M{R}^2}{9}$
• C. $\frac{3M{R}^2}{8}$
• D. $\frac{17M{R}^2}{18}$

Answer 1

The correct option is D $\frac{17M{R}^2}{18}$

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=2R/3

$I=M{R}^2/2+M\times 4R^2/9=\frac{17M{R}^2}{18}$