Question

M.I of hemisphere about axis $2$, which is parallel to diameter but passing through centre of mass, will be

• A. $\frac{83}{320}m{R}^2$
• B. $\frac{2}{5}m{R}^2$
• C. $\frac{m{R}^2}{5}$
• D. $\frac{2}{3}m{R}^2$

Answer 1

The correct option is A $\frac{83}{320}m{R}^2$

Moment of inertia about axis $\perp$ is

$I_1=\frac{2}{5}m{R}^2$

Now moment of inertia about axis $2$ is (which is passing through C.M).

$I_2=I_1-m{\left(\frac{3R}{Q}\right)}^2$

$=\frac{2}{5}m{R}^2-\frac{9}{64}m{R}^2$

$I_2=m{R}^2(\frac{2}{5}-\frac{9}{64})$

$I_2=m{R}^2\left(\frac{83}{320}\right)$