Four spheres of diameter a and mass m each are arranged at the corners of a square of side 1. Calculate the moment of inertia of the system about CD taken as its axis.

Explanation

To calculate the moment of inertia of the system of four spheres arranged at the corners of a square about the axis CD, we can follow these steps:

### Step 1: Understand the arrangement
We have four spheres, each with mass \( m \) and diameter \( a \), positioned at the corners of a square with side length \( 1 \). We will denote the corners as A, B, C, and D.

### Step 2: Identify the axis of rotation
The axis of rotation is taken along the line CD. This means that the spheres at points C and D will have their moment of inertia calculated differently than those at points A and B.

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