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 BB'

Explanation

To solve the problem of calculating the moment of inertia of four spheres placed at the corners of a square about the axis BB', we can follow these steps:

### Step 1: Understand the Configuration
We have four spheres, each of mass \( M \) and diameter \( 2a \), placed at the corners of a square with side length \( b \). The axis BB' is perpendicular to the plane of the square and passes through the center of the square.

### Step 2: Moment of Inertia of a Single Sphere
The moment of inertia \( I \) of a solid sphere about an axis through its center is given by the formula:
\[
...