Calculate the moment of inertia of a hollow cylinder of mass M and radius R about a line parallel to the axis of the cylinder and on the surface of the cylinder?

Explanation

To calculate the moment of inertia of a hollow cylinder of mass \( M \) and radius \( R \) about a line parallel to the axis of the cylinder and on the surface of the cylinder, we can follow these steps:

### Step 1: Understand the Geometry
A hollow cylinder can be visualized as a cylindrical shell with a certain mass and radius. The moment of inertia (I) is a measure of how difficult it is to change the rotational motion of the object about a given axis.

### Step 2: Moment of Inertia about the Central Axis
The moment of inertia of a hollow cylinder about its central axis (which is perpendicular to the circular faces) is given by the formula:
\[
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