Q129 / 170 · Manipal (MET) 2021 · Physics
A solid sphere of radius $R$ has moment of inertia / about its diameter. What will be moment of inertia of a shell of same mass and same radius about its diameter ?
- A$\frac{3}{5}$ ।
- Correct answerB$\frac{5}{3}$ ।
- C$\frac{2}{3}$ ।
- D$\frac{2}{5}$ ।
Solution
For a solid sphere,
$I=\frac{2}{5} M R^2$
For a spherical shell, $\begin{aligned} I^{\prime} & =\frac{2}{3} M R^2 \\ & =\frac{5}{3} \times \frac{2}{5} M R^2=\frac{5}{3} I\end{aligned}$
For a spherical shell, $\begin{aligned} I^{\prime} & =\frac{2}{3} M R^2 \\ & =\frac{5}{3} \times \frac{2}{5} M R^2=\frac{5}{3} I\end{aligned}$
Hence, the correct answer is option: 'B'.