When there is no external torque acting on a body moving in an elliptical path, which of the following quantities remain constant ?

Options

A. Kinetic energy
B. Potential energy
C. Linear momentum
D. Angular momentum

Answer

To solve the problem, we need to analyze the situation where a body is moving in an elliptical path without any external torque acting on it. We will determine which quantities remain constant under these conditions.

### Step-by-Step Solution:

1. **Understanding the System**:
- We have a body moving in an elliptical path.
- There is no external torque acting on the body.

2. **Applying the Principle of Angular Momentum**:
- According to the principle of conservation of angular momentum, if no external torque is acting on a system, the angular momentum of that system remains constant.
- Mathematically, this can be expressed as:
\[ \tau_{\text{net}} = \frac{dL}{dt} \]
where \( \tau_{\text{net}} \) is the net external torque and \( L \) is the angular momentum.

3. **Analyzing the Given Condition**:
- Since it is given that there is no external torque (\( \tau_{\text{net}} = 0 \)), we can conclude:
\[ \frac{dL}{dt} = 0 \]
- This implies that the angular momentum \( L \) is constant over time.

4. **Conclusion**:
- Therefore, the quantity that remains constant when there is no external torque acting on the body is the **angular momentum**.

5. **Final Answer**:
- The correct answer is **angular momentum**.