Question

Mi 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 $\frac{2}{5}m{R}^2$

$\begin{array}{c}\text{Let us assume a splere of mass}=2M\\ \text{and radius}=R\\ \text{Therefore-}\\ \text{we know that}\left(I\right)\text{of Sphere}=\frac{2}{5}M{R}^2\\ I\to \text{Moment of Inertia}\\ \text{If we divide the sphere into two parts}\\ \text{to form a hemisphere then}\\ \text{I nemisphere}=\frac{\text{Isprere}}{2}\end{array}$

$\begin{array}{c}\Rightarrow \text{Ihemisphere}=\frac{1}{2}\times \frac{4}{5}M{R}^2=\frac{2}{5}M{R}^2\\ \text{and the mass of the Hemisphere remains (M)}\end{array}$