When a torque acting on a system is increased, then which óne of the following quantities will increase? (a) linear momentum (b) Angular momentum (c) force (d) Displacement

Options

A. linear momentum
B. Angular momentum
C. force
D. Displacement

Answer

To solve the question, we need to analyze the relationship between torque and angular momentum.

### Step-by-Step Solution:

1. **Understand the Concept of Torque**:
Torque (\( \tau \)) is defined as the rate of change of angular momentum (\( L \)) with respect to time. Mathematically, this is expressed as:
\[ \tau = \frac{dL}{dt} \]
This means that if torque is applied to a system, it will change the angular momentum of that system over time.

2. **Relate Torque to Angular Momentum**:
From the equation \( \tau = \frac{dL}{dt} \), if the torque acting on a system is increased, it implies that the rate of change of angular momentum is also increased. This means that the angular momentum itself will increase over time if torque is applied continuously.

3. **Analyze the Options**:
- (a) Linear momentum: This is not directly related to torque; hence it may not increase.
- (b) Angular momentum: As established, if torque increases, angular momentum also increases.
- (c) Force: Torque is related to force, but increasing torque does not necessarily mean that the force itself increases.
- (d) Displacement: Displacement is not directly affected by torque.

4. **Conclusion**:
Based on the relationship between torque and angular momentum, the correct answer is:
\[ \text{(b) Angular momentum} \]