Question

The moment of inertia of a non-uniform semicircular wire having mass m and radius r about a line perpendicular to the plane of the wire through the center is

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

Answer 1

The correct option is A $m{r}^2$

Moment of inertia of every small element is $dm{r}^2$

$\Rightarrow dI=dm{r}^2$

$\Rightarrow I=\int dm{r}^2$

$\Rightarrow I=m{r}^2$

Therefore, A is correct option.