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. $\frac{1}{2}{mr}^2$
• B. $\frac{1}{4}{mr}^2$
• C. $\frac{1}{2}{mr}^2+{mx}^2$
• D. $\frac{1}{2}{mr}^2-{mx}^2$

Answer 1

The correct option is B $\frac{1}{4}{mr}^2$

$2I_{semicircle}=I_{circle}=\frac{m{r}^2}{2}$

$I_{semicircle}=\frac{m{r}^2}{4}$