Question

A semicircular 2-dimensional plate of mass $m$ has radius $r$ and centre C. Its centre of mass is at a distance $x$ from C. Its moment of inertia about an axis through its centre of mass and perpendicular to its plane is

• A. $\frac{1}{2}m{r}^2$
• B. $\frac{1}{4}m{r}^2$
• C. $\frac{1}{2}m{r}^2+m{x}^2$
• D. $\frac{1}{2}m{r}^2-m{x}^2$

Answer 1

The correct option is D $\frac{1}{2}m{r}^2-m{x}^2$

Moment of inertia of semicircular disc about C is
$\therefore \{I_C{\}}_{semicircle}=\frac{1}{2}m{r}^2$
Using parallel axis theorem
$I_C=I_{CM}+m{x}^2$
$\therefore I_{CM}=\frac{1}{2}m{r}^2-m{x}^2$.