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: Use radius of gyration
Tangent in-plane for disc: $k^2 = \frac{R^2}{4}+R^2 = \frac54R^2$. So $I = \frac M2\cdot\frac54R^2 = \frac58MR^2$.

Step 2: Sphere
$k^2 = \frac25R^2+R^2 = \frac75R^2$, so $I = \frac75MR^2$.

Step 3: Divide
$\frac58\div\frac75 = \frac{25}{56}$. Option (B).

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