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

To find the moment of inertia of four particles each of mass \( m \) located at the corners of a square of edge length \( a \) about an axis perpendicular to the plane of the square and passing through its center, we can follow these steps:

### Step 1: Determine the distance of each mass from the axis of rotation
The axis of rotation is perpendicular to the plane of the square and passes through its center. The distance from the center of the square to any corner (where the mass is located) can be calculated using the Pythagorean theorem.

For a square with edge length \( a \), the distance \( r \) from the center to a corner is given by:
\[
r = \frac{a}{\sqrt{2}}
...