Question

M.I of hemisphere about axis $3$, which is also parallel to the diameter;

• A. $\frac{2}{5}m{R}^2$
• B. $\frac{m{R}^2}{5}$
• C. $\frac{173}{320}m{R}^2$
• D. $\frac{2}{3}m{R}^2$

Answer 1

The correct option is A $\frac{2}{5}m{R}^2$

Now moment of inertia $I_2$ which is passing through its centre of mass is

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

Now by parallel axis theorem

$I_3=I_2+m{\left(\frac{3}{8}R\right)}^2$

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

$I_3=m{R}^2(\frac{2}{5}-\frac{9}{64}+\frac{9}{64})=\frac{2}{5}m{R}^2$