Question

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

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

Answer 1

Answer: (A)

$\frac{1}{2}M{r}^2$

If ${}^{\prime }{M}^{\prime }$ is the mass of the semi-circular disc, then the mass of the complete disc will be $2M$.
Moment of inertia of complete disc about the given axis
$=\frac{1}{2}\left(2M\right)r^2=M{r}^2$

The moment of inertia of the semi-circular disc is half of the Moment of inertia of the circular disc due to symmetry.
Moment of inertia of semi-circular disc $=\frac{1}{2}M{r}^2$
So, (D) is the right choice.