Four particles each of mass m are kept at the four corners of a square of edge a. Find the moment of inertias of the system about a line perpendicular to the plane of the square and passing through the centre of the square.

Explanation

The perpendicular distance of every particle from the given line is `a//sqrt(2)`. The moment of inertia of one particle is therefore, `m(a//sqrt(2))^(2)=1/2ma^(2)`. The moment of inertia of the system is, therefore.
`4xx1/2ma^(2)=2ma^(2)`