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

Answer 1

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

The moment of inetia of the disc is given by:

$I_{wholedisc}=\frac{1}{2}\left(2M\right)r^2=M{r}^2$

In half-disc, the mass is reduced to M.

$\therefore I_{Halfdisc}=\frac{1}{2}M{r}^2$