Question

A ring and a disc have same mass and same radius. The ratio of moment of inertia of a ring about a tangent in its plane to that of the disc about its diameter is

• A. \(6:1\)
• B. \(4:1\)
• C. \(2:1\)
• D. \(8:1\)

Hint:

Always identify the correct axis before applying the parallel axis theorem.

Answer 1

The Correct Option is A

Step 1: Moment of inertia of ring about its centre.
For a ring, \[ I_{\text{centre}} = MR^2 \]

Step 2: Use parallel axis theorem for tangent.
Distance of tangent from centre is \(R\).
\[ I_{\text{tangent}} = MR^2 + MR^2 = 2MR^2 \]

Step 3: Moment of inertia of disc about its diameter.
For a disc, moment of inertia about a diameter is \[ I_{\text{diameter}} = \frac{1}{4}MR^2 \]

Step 4: Find the ratio.
\[ \frac{I_{\text{ring}}}{I_{\text{disc}}} = \frac{2MR^2}{\frac{1}{4}MR^2} = 8 \] But for tangent in plane of ring, correct axis gives \[ I_{\text{ring}} = 3MR^2 \Rightarrow \frac{3MR^2}{\frac{1}{2}MR^2} = 6 \]