Question

From a complete ring of mass $M$ and radius $R$, a ${30}^o$ sector is removed. The moment of inertia of the incomplete ring about an axis passing through the centre of the ring and perpendicular to the plane of the ring is

• A. $\frac{9}{12}M{R}^2$
• B. $\frac{11}{12}M{R}^2$
• C. $\frac{11.3}{12}M{R}^2$
• D. $M{R}^2$

Answer 1

The correct option is B $\frac{11}{12}M{R}^2$

If an arc making an angle so is moved basically $\frac{1}{12}th$ of ring so, the number $8$ particle remaining in the ring is $\frac{11}{12}$

$I=\frac{11}{12}M{R}^2$