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

Explanation

To analyze the assertion and reason provided in the question, we will break down the concepts of relative velocity in the context of head-on elastic collisions.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that the relative velocity of two particles in a head-on elastic collision remains unchanged in both magnitude and direction.
- In an elastic collision, the total kinetic energy and momentum are conserved.

2. **Understanding the Reason**:
- The reason states that while the relative velocity is unchanged in magnitude, it gets reversed in direction.
- This implies that the relative velocity before the collision is equal in magnitude but opposite in direction to the relative velocity after the collision.

3. **Relative Velocity in Elastic Collisions**:
- In a head-on elastic collision, if two particles have initial velocities \( v_1 \) and \( v_2 \), the relative velocity of approach is given by \( v_{rel, approach} = v_1 - v_2 \).
- After the collision, the velocities change to \( v_1' \) and \( v_2' \), and the relative velocity of separation is given by \( v_{rel, separation} = v_2' - v_1' \).

4. **Coefficient of Restitution**:
- The coefficient of restitution \( e \) for elastic collisions is 1, which means:
\[ e = \frac{v_{rel, separation}}{v_{rel, approach}} = 1 \]
- Thus, \( v_{rel, separation} = v_{rel, approach} \).

5. **Magnitude and Direction**:
- While the magnitudes of the relative velocities before and after the collision are equal, their directions are opposite.
- This means that if the particles are moving towards each other before the collision, they will be moving away from each other after the collision.

6. **Conclusion**:
- Therefore, the assertion is incorrect because it claims that the direction of the relative velocity remains unchanged.
- The reason is correct as it states that the magnitude remains the same but the direction is reversed.

### Final Answer:
- The assertion is **false** and the reason is **true**. Thus, the correct option is that the assertion is false while the reason is true.