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

Answer: (D)

The mass of complete (circular) disc is
The moment of inertia of disc about the given axis is
$I=\frac{2M{r}^2}{2}<br/>=M{r}^2$
Let, the moment of inertia of semicircular disc is $I_1$ The disc may be assumed as combination of two semicircular parts.
Thus, $I_1=I-I_1$
$\therefore I_1=\frac{I}{2}=\frac{M{r}^2}{2}$