Why does a solid sphere have smaller moment of inertia than a hollow cylinder of same mass and radius, about an axis passing through their axes of symmentry ?

Explanation

To understand why a solid sphere has a smaller moment of inertia than a hollow cylinder of the same mass and radius about an axis passing through their axes of symmetry, we can break down the explanation into several steps.

### Step-by-Step Solution:

1. **Understanding Moment of Inertia**:
- The moment of inertia (I) is a measure of an object's resistance to changes in its rotation. It is defined mathematically as:
\[
I = \int r^2 \, dm
...