Question

Moment of inertia of hemispherical shell of mass M and radius R about axis passing through its center of mass as shown in figure is $\frac{5}{3x}M{R}^2$. Here x is

Answer 1

By Parallel Axis Theorem:
$I=I_{cm}+M{\left(\frac{R}{2}\right)}^2$

$\frac{2}{3}M{R}^2=I_{cm}+\frac{M{R}^2}{4}$

$I_{cm}=(\frac{2}{3}-\frac{1}{4})M{R}^2$

$I_{cm}=\left(\frac{8-3}{12}\right)M{R}^2=\frac{5}{12}M{R}^2$