Question

The moment of inertia of a uniform semicircular wire of mass $m$ and radius $r$, about an axis passing through its centre of mass and perpendicular to its plane is

• A. $\frac{m r^{2}}{2}$
• B. $m r^{2}$
• C. $m r^{2}\left(1-\frac{4}{\pi^{2}}\right)$
• D. $m r^{2}\left(1+\frac{4}{\pi^{2}}\right)$

Answer 1

Answer: (C)

$m r^{2}=I_{c m}+m\left(\frac{2 r}{\pi}\right)^{2}$
$I_{c m}=m r^{2}\left[1-\frac{4}{\pi^{2}}\right]$