Assertion: During head on collision between two bodies let `Deltap_1` is change in momentum of first body and `Deltap_2` the change in momentum of the other body, then `Deltap_1=Deltap_2`.
Reason: Total momentum of the system should remain constant.

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 solve the problem, we need to analyze the assertion and the reason provided in the question regarding the head-on collision between two bodies.

### Step-by-Step Solution:

1. **Understanding the Assertion**: The assertion states that during a head-on collision between two bodies, the change in momentum of the first body (Δp₁) is equal to the change in momentum of the second body (Δp₂). Mathematically, this can be written as:
\[ \Delta p_1 = \Delta p_2 \]

2. **Understanding the Reason**: The reason given is that the total momentum of the system should remain constant. This is a fundamental principle of physics known as the conservation of momentum, which states that in the absence of external forces, the total momentum of a closed system remains constant.

3. **Applying Conservation of Momentum**: In a collision, the total momentum before the collision must equal the total momentum after the collision. If we denote the initial momenta of the two bodies as \(p_{1i}\) and \(p_{2i}\), and their final momenta as \(p_{1f}\) and \(p_{2f}\), we can write:
\[ p_{1i} + p_{2i} = p_{1f} + p_{2f} \]

4. **Change in Momentum**: The change in momentum for each body can be defined as:
\[ \Delta p_1 = p_{1f} - p_{1i} \]
\[ \Delta p_2 = p_{2f} - p_{2i} \]

5. **Total Change in Momentum**: The total change in momentum of the system can be expressed as:
\[ \Delta p_{system} = \Delta p_1 + \Delta p_2 \]
Since momentum is conserved, we have:
\[ \Delta p_{system} = 0 \]

6. **Relating Changes in Momentum**: From the equation above, we can derive:
\[ \Delta p_1 + \Delta p_2 = 0 \implies \Delta p_1 = -\Delta p_2 \]
This indicates that the change in momentum of one body is equal in magnitude and opposite in direction to the change in momentum of the other body.

7. **Conclusion**: Since the assertion states that Δp₁ = Δp₂, which contradicts our derived conclusion that Δp₁ = -Δp₂, we can conclude that the assertion is false. However, the reason is true as it correctly states the principle of conservation of momentum.

### Final Answer:
- **Assertion**: False
- **Reason**: True