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 1: Understand the Geometry of the Cylinder
We have a uniform cylinder with mass \( M \) and radius \( R \). The height of the cylinder is \( h \). We need to find the moment of inertia about an axis that passes through the center of mass and is perpendicular to the base.

### Step 2: Set Up the Moment of Inertia Integral
The moment of inertia \( I \) is given by the integral:
\[
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