Identify the case when an elastic metal rod does not undergo elongation

Options

A. it is pulled with a constant acceleration on a smooth horizontal surface
B. it is pulled with constant acceleration on a smooth horizontal surface
C. it is allowed to fall freely
D. All of the above

Explanation

To solve the question, "Identify the case when an elastic metal rod does not undergo elongation," we can analyze the provided options step by step.

### Step-by-Step Solution:

1. **Understanding Elasticity**:
- Elasticity refers to the ability of a material to return to its original shape after the removal of an external force. When a force is applied to an elastic material, it may undergo elongation or deformation.

2. **Analyzing the Options**:
- We need to consider different scenarios in which an elastic metal rod may or may not elongate.

3. **Option A: Pulled with Constant Acceleration on a Smooth Horizontal Surface**:
- If the rod is pulled with a constant acceleration, it experiences a force along its length, which would cause it to elongate.
- **Conclusion**: This option would result in elongation.

4. **Option B: Pulled with Constant Acceleration on a Smooth Horizontal Surface** (repeated):
- Similar to Option A, pulling the rod with constant acceleration will cause elongation.
- **Conclusion**: This option would also result in elongation.

5. **Option C: Allowed to Fall Freely**:
- When the rod is allowed to fall freely, it is in a state of free fall. In this case, there is no external force acting on the rod that would cause elongation.
- The only force acting on it is gravity, which does not stretch the rod.
- **Conclusion**: This option will not result in elongation.

6. **Option D: Not Provided, but Assuming Similar to A and B**:
- If this option is similar to A and B, it would also cause elongation.
- **Conclusion**: This option would likely result in elongation as well.

### Final Answer:
The case when an elastic metal rod does not undergo elongation is **Option C: Allowed to fall freely**.

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