Four spheres each of mass M and diameter 2a are placed at the corners of square of side b as shown below. Calculate the moment of inertia about axis AA'

Explanation

To calculate the moment of inertia of four spheres, each of mass \( M \) and diameter \( 2a \), placed at the corners of a square of side \( b \) about the axis AA', we will follow these steps:

### Step 1: Identify the Moment of Inertia of a Single Sphere about its Center of Mass
The moment of inertia \( I_{CM} \) of a solid sphere about its center of mass is given by the formula:
\[ I_{CM} = \frac{2}{5} M r^2 \]
where \( r \) is the radius of the sphere. Given that the diameter is \( 2a \), the radius \( r \) is:
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