Question

If 27 identical smaller spheres each of moment of inertia I about diametrical axis are combined to form a bigger sphere, then the moment of inertia of the bigger sphere about its diameter is

• A. 243 I
• B. 81 I
• C. 27 I
• D. 9 I

Answer 1

The correct option is A 243 I

$\begin{array}{c}I=\frac{2}{5}m{r}^2\\ M=27m\\ \frac{4}{3}\pi R^3=27.\frac{4}{3}\pi r^3\\ R=3r\\ I^{\prime }=\frac{2}{5}\left(27m\right).\left(9r^2\right)\\ =\left(27\times 9\right)I\\ =243I\end{array}$

Option $A$ is correct .