State the expression for the moment of inertia of a solid cylinder of uniform cross section about an axis through its centre and perpendicular to its length.

Explanation

To find the expression for the moment of inertia of a solid cylinder of uniform cross-section about an axis through its center and perpendicular to its length, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Geometry of the Cylinder**:
- Consider a solid cylinder with mass \( m \) and radius \( r \). The axis of rotation is through the center of the cylinder and perpendicular to its length.

2. **Use the Formula for Moment of Inertia**:
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