There are four solid balls with their centres at the four corners of a square of side `a`. the mass of each sphere is `m` and radius is `r`. Find the moment of inertia of the system about one of the sides of the square

Options

A. `(8)/(5)mr^(2)+2ma^(2)`
B. `(5)/(8)mr^(2)+2ma^(2)`
C. `(8)/(5)mr^(2)+ma^(2)`
D. `(8)/(5)mr^(2)+4ma^(2)`

Explanation

To find the moment of inertia of the system of four solid balls located at the corners of a square about one of the sides of the square, we can follow these steps:

### Step 1: Understand the Configuration
We have four solid balls, each with mass \( m \) and radius \( r \), located at the corners of a square with side length \( a \). We need to find the moment of inertia about one of the sides of the square, say side AA'.

### Step 2: Identify the Moment of Inertia of One Ball
The moment of inertia \( I \) of a solid sphere about its own center is given by the formula:
\[
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