Question

The moment of inertia of a uniform semicircular disc of mass $M$ and radius $R$ about a line perpendicular to the plane of disc and passing through the centre is :

• A. $\frac{M{R}^4}{4}$
• B. $\frac{2}{5}M{R}^2$
• C. $M{R}^2$
• D. $\frac{M{R}^2}{2}$

Answer 1

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

If we consider the circular disc we see that its mass is $2M$ and its moment of inertia about the center would be $\frac{\left(2M\right)R^2}{2}=M{R}^2$
Thus moment of inertia of half of this disc would be $\frac{M{R}^2}{2}$