Question

The moment of inertia of a solid hemi-sphere of mass M and radius R about an axis passing through its center of mass and parallel to its circular face is

• A. $\frac{9M{R}^2}{64}$
• B. $\frac{83M{R}^2}{320}$
• C. $\frac{2M{R}^2}{5}$
• D. $\frac{M{R}^2}{5}$

Answer 1

The correct option is B $\frac{83M{R}^2}{320}$


From the parallel axis theorem,
$I_{AB}=I_{CD}+M{\left(\frac{3R}{8}\right)}^2$
$\Rightarrow I_{CD}=I_{AB}–\frac{9M{R}^2}{64}$
$=\frac{2}{5}M{R}^2–\frac{9M{R}^2}{64}$
$=\frac{83M{R}^2}{320}$