Question

A solid hemisphere (m, R) has the moment of inertia about axis 1 (Diameter of hemisphere)

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

Answer 1

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

Let the solid hemisphere has moment of inertia, I about the vertical axis passing through their base centers. Now, if I displace them parallel to the axis and join them to complete a sphere then $2I=\frac{2}{5}m{R}^2$

or $I=\frac{1}{5}m{R}^2$

Hence, the answer is $\frac{m{R}^2}{5}.$