Question

The figure shows a small portion of mass m of a circular disc radius R. If this section subtends an angle of ${30}^o$, then its moment of inertia about an axis perpendicular to the plane and passing through the centre of the circle

• A. $m{R}^2$
• B. $\frac{11}{12}m{R}^2$
• C. $\frac{1}{12}m{R}^2$
• D. $\frac{1}{24}m{R}^2$

Answer 1

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

Generally MOI denoted by = $M{R}^2$

But an arc of Disc is removed

Now an arc substending ${30}^{\circ }$ is removed which is

equal to ${\frac{1}{2}}^{th}$ part of Disc

Remaining will be = ${\frac{11}{12}}^{th}$ part

Thus MOI of final part will be = $\frac{11}{12}M{R}^2$