Question

The moment of inertia of semicircular ring about an axis which is perpendicular to the plane of the ring and passes through the center.

• A. $M{R}^2$
• B. $\frac{M{R}^2}{2}$
• C. $\frac{M{R}^2}{4}$
• D. None of these

Answer 1

The correct option is A $M{R}^2$

It is just MR^2, where M is the mass and R is the radius of the circle.

All the mass is at the same distance from the center, and so the total rotational inertia is just the total mass times the square of the radius.

Here, “through the center of the circle of which the semi-circle is half” means“through the center”.