Assertion: The relative velocity of the two particles in head-on elastic collision is unchanged both in magnitude and direction.
Reason: The relative velocity is unchanged in magnitude but gets reversed in direction.

Options

A. (a) If both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
B. (b) If both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.
C. (c) If Assertion is true but Reason is false.
D. (d) If Assertion is false but Reason is true.

Explanation

To solve the question regarding the assertion and reason related to the relative velocity of two particles in a head-on elastic collision, we will analyze both statements step by step.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states: "The relative velocity of the two particles in head-on elastic collision is unchanged both in magnitude and direction."
- In an elastic collision, the relative velocity of approach (before the collision) is equal to the relative velocity of separation (after the collision) but in opposite directions. Thus, the assertion is incorrect because while the magnitude remains the same, the direction does change.

2. **Understanding the Reason**:
- The reason states: "The relative velocity is unchanged in magnitude but gets reversed in direction."
- This statement is true. In a head-on elastic collision, the magnitude of the relative velocity remains the same, but the direction is reversed after the collision.

3. **Evaluating the Relationship**:
- The assertion is false because it claims that the direction remains unchanged, which is not the case.
- The reason is true as it correctly describes the behavior of relative velocity in an elastic collision.

4. **Conclusion**:
- Since the assertion is false and the reason is true, the correct option is D: "Assertion is false but reason is true."

### Final Answer:
The correct option is D: "Assertion is false but reason is true."