Question

Four spheres, each of radius a and mass m, are placed with their centre on four corners of a square of side b. Calculate the moment of inertia of the arrangement about any side of the square.

Answer 1

Moment of inertia about center of mass= $I_{cm}$= $\frac{2}{5}M{a}^2$

(Where, a is the radius of the sphere)

If one side of the sphere is taken an axis, then moment of inertia about axis is

I= $I_{cm}+M{b}^2$

= $\frac{2}{5}M{a}^2+M{b}^2$

$I_{net}=2\left(\frac{2}{5}M{a}^2\right)+2(\frac{2}{5}M{a}^2+M{b}^2)$

$I_{net}$ =$\frac{8}{5}M{a}^2+2M{b}^2$