Find the moment of inertia of a uniform cylinder about an axis through its centre of mass and perpendicular to its base. Mass of the cylinder is M and radius is R.

Explanation

To find the moment of inertia of a uniform cylinder about an axis through its center of mass and perpendicular to its base, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Geometry**:
- We have a uniform cylinder with mass \( M \) and radius \( R \). The axis of rotation is through its center and perpendicular to its base.

2. **Use the Definition of Moment of Inertia**:
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