Two identical spheres each of mass 1.20 kg and radius 10.0 cm are fixed at the ends of a light rod so that the separation between the centers is 50.0 cm. Find the moment of inertia of the system about an axis perpendicular to the rod passing through its middle point.

Explanation

To find the moment of inertia of the system consisting of two identical spheres fixed at the ends of a light rod, we can follow these steps:

### Step 1: Understand the Problem
We have two identical spheres, each with a mass of \( m = 1.20 \, \text{kg} \) and a radius of \( r = 10.0 \, \text{cm} = 0.1 \, \text{m} \). The distance between the centers of the spheres is \( d = 50.0 \, \text{cm} = 0.5 \, \text{m} \). We need to find the moment of inertia about an axis that is perpendicular to the rod and passes through its midpoint.

### Step 2: Use the Parallel Axis Theorem
The moment of inertia \( I \) about an axis parallel to the axis through the center of mass is given by the parallel axis theorem:
\[
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