Question

A same torque is applied to a disc and a ring of equal mass and radii then

• A. the ring will rotate with greater angular frequency.
• B. both will rotate with same angular frequency.
• C. the disc will rotate with greater angular frequency.
• D. both will rotate with same angular velocity.

Hint:

Lower moment of inertia results in higher angular acceleration for the same torque.

Answer 1

The Correct Option is C

Step 1: Concept
Torque $\tau = I\alpha$, where $I$ is moment of inertia and $\alpha$ is angular acceleration.

Step 2: Analysis
- $I_{\text{ring}} = MR^2$
- $I_{\text{disc}} = \frac{1}{2}MR^2$
Since $I_{\text{ring}} > I_{\text{disc}}$, for the same torque, $\alpha_{\text{disc}} > \alpha_{\text{ring}}$.

Step 3: Calculation
Higher angular acceleration leads to a higher change in angular velocity and frequency in the same time interval.

Step 4: Conclusion
Hence, the disc will rotate with greater angular frequency. Final Answer: (C)