Question:
Four identical solid spheres each of mass ' $m$ ' and radius ' $a$ ' are placed with their centres on the four corners of a square of side ' $b$ '. The moment of inertia of the system about one side of square where the axis of rotation is parallel to the plane of the square is :
Correct Option: , 4
Solution:
$I=\frac{2}{5} m a^{2}+\frac{2}{5} m a^{2}+\left[\frac{2}{5} m a^{2}+m b^{2}\right]+\frac{2}{5} m a^{2}+m b^{2}$
$I=4 \times \frac{2}{5} m a^{2}+2 m b^{2}$
$=\frac{8}{5} m a^{2}+2 m b^{2}$