Find the moment of inertia of a uniform ring of mass M and radius R about a diameter.

Explanation

To find the moment of inertia of a uniform ring of mass \( M \) and radius \( R \) about a diameter, we can use the Perpendicular Axis Theorem. Here’s a step-by-step solution:

### Step 1: Understand the Perpendicular Axis Theorem
The Perpendicular Axis Theorem states that for a planar body lying in the XY-plane, the moment of inertia about an axis perpendicular to the plane (Z-axis) is equal to the sum of the moments of inertia about two mutually perpendicular axes (X-axis and Y-axis) lying in the plane. Mathematically, it is given by:
\[ I_z = I_x + I_y \]

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