Moment of inertia of a ring of mass M and radius R about an axis passing through the centre and perpendicular to the plane is I. What is the moment of inertia about its diameter ?

Options

A. I
B. `I//2`
C. `I//sqrt2`
D. `I+MR^2`

Explanation

To find the moment of inertia of a ring of mass \( M \) and radius \( R \) about its diameter, we can use the perpendicular axis theorem. Let's go through the steps:

### Step 1: Understand the Moment of Inertia about the Axis
The moment of inertia of a ring about an axis passing through the center and perpendicular to its plane is given as \( I \).

### Step 2: Apply the Perpendicular Axis Theorem
The perpendicular axis theorem states that for a planar body, the moment of inertia about an axis perpendicular to the plane (let's call it \( I_z \)) is equal to the sum of the moments of inertia about two perpendicular axes in the plane (let's call them \( I_x \) and \( I_y \)):
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