Question

A solid sphere of mass M and a disc of mass \(\frac{M}{2}\) have the same radius. The ratio of moment of inertia of the disc about a tangent in its plane to the moment of inertia of the sphere about its tangent will be

• A. \(15:8\)
• B. \(25:56\)
• C. \(12:7\)
• D. \(16:9\)

Hint:

Use the parallel axis theorem for both bodies.

Answer 1

The Correct Option is B

Step 1: Disc of mass M/2
About a diameter, \(I = \frac14\left(\frac M2\right)R^2\). A tangent in the plane is at distance \(R\) from the diameter, so \(I_{disc} = \frac{MR^2}{8} + \frac M2R^2 = \frac{5MR^2}{8}\).

Step 2: Solid sphere
About a diameter, \(I = \frac25MR^2\). About a tangent: \(I_{sphere} = \frac25MR^2 + MR^2 = \frac75MR^2\).

Step 3: Ratio
\[ \frac{I_{disc}}{I_{sphere}} = \frac{5/8}{7/5} = \frac{25}{56} \]
Option (B).

Final Answer:
The ratio is 25:56. \[ \boxed{\text{(B)}\ 25:56} \]