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: Understanding the Question:
We need to compare the rotational response of a disc and a ring when the same torque is applied to them.

Step 2: Key Formula or Approach:
1. Newton's Second Law for rotation: \( \tau = I \alpha \).
2. Moment of inertia of a disc: \( I_{\text{disc}} = \frac{1}{2} MR^2 \).
3. Moment of inertia of a ring: \( I_{\text{ring}} = MR^2 \).

Step 3: Detailed Explanation:
Given that mass \( M \) and radius \( R \) are the same for both.
Clearly, \( I_{\text{disc}} < I_{\text{ring}} \).
Since the same torque \( \tau \) is applied to both, the angular acceleration \( \alpha = \frac{\tau}{I} \).
Because \( I_{\text{disc}} \) is smaller, \( \alpha_{\text{disc}} > \alpha_{\text{ring}} \).
Starting from rest, the angular velocity after time \( t \) is \( \omega = \alpha t \).
Thus, \( \omega_{\text{disc}} > \omega_{\text{ring}} \).
Since angular frequency \( f \propto \omega \), the disc will have a higher frequency.

Step 4: Final Answer:
The disc will rotate with a greater angular frequency.