Question

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

• A. $\frac{1}{4}M{r}^2$
• B. $\frac{2}{5}M{r}^2$
• C. $M{r}^2$
• D. $\frac{1}{2}M{r}^2$

Answer 1

The correct option is D $\frac{1}{2}M{r}^2$

A circular disc will have 2 times the mass of the semicircular disc.
Moment of inertia of circular disc of mass $2M$ is
$I_{circulardisc}=\frac{1}{2}\left(2M\right)R^2=M{R}^2$
Moment of inertia of semi-circular disc is half of the Moment of inertia of circular disc due to symmetry.
$\therefore I_{semicirculardisc}=\frac{1}{2}{I}_{circulardisc}=\frac{1}{2}M{R}^2$