When a torque acting upon a system is zero, which of the following will be constant ?

Options

A. Force
B. Linear impulse
C. Linear momentum
D. Angular momentum

Explanation

To solve the question, we need to analyze the conditions under which torque is zero and determine what physical quantities remain constant in such a scenario.

### Step-by-Step Solution:

1. **Understanding Torque**:
- Torque (\( \tau \)) is defined as the product of the force (\( F \)) and the distance (\( r \)) from the pivot point to the point where the force is applied, and it is given by the formula:
\[ \tau = r \times F \]
- When the torque acting on a system is zero, it implies that either the net force acting on the system is zero or the forces are balanced in such a way that their moments about the pivot point cancel each other out.

2. **Analyzing Forces**:
- If the torque is zero, it does not mean that the forces are zero. Forces can still be acting on the system, but they do not create a net torque about the center of mass or the pivot point.

3. **Linear Momentum**:
- If there are external forces acting on the system, linear momentum may not be conserved. Linear momentum (\( p \)) is given by:
\[ p = mv \]
- If there is a net external force, linear momentum will change.

4. **Angular Momentum**:
- Angular momentum (\( L \)) is given by:
\[ L = I \omega \]
- Where \( I \) is the moment of inertia and \( \omega \) is the angular velocity. If the torque is zero, the angular momentum of the system is conserved. This means that:
\[ \frac{dL}{dt} = 0 \implies L = \text{constant} \]

5. **Conclusion**:
- When the torque acting on a system is zero, the quantity that remains constant is the angular momentum of the system.

### Final Answer:
The correct answer is **angular momentum**.