Assertion : The rate of change of total momentum of a many particle system is proportional to the sum of the internal forces of the system.
Reason : Internal forces can change the kinetic energy but not the momentum of the system.

Options

A. If both assertion and reason are true and the reason is the correct explanation of the assertion.
B. If both assertion and reason are true but reason is not the correct explanation of the assertion.
C. If assertion is true but reason is false.
D. If assertion is false but reason is true.

Explanation

To solve the question, we need to analyze the assertion and the reason provided.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that "The rate of change of total momentum of a many-particle system is proportional to the sum of the internal forces of the system."
- According to Newton's second law, the rate of change of momentum of a system is equal to the net external force acting on it. Internal forces act between particles of the system and do not affect the total momentum of the system.

**Conclusion**: The assertion is **false** because the rate of change of momentum is not influenced by internal forces.

2. **Understanding the Reason**:
- The reason states that "Internal forces can change the kinetic energy but not the momentum of the system."
- This is true because internal forces can indeed change the distribution of kinetic energy among the particles but do not change the total momentum of the system. The total momentum remains constant if no external forces are acting.

**Conclusion**: The reason is **true**.

3. **Final Evaluation**:
- Since the assertion is false and the reason is true, we conclude that the correct answer to the question is that the assertion is false while the reason is true.

### Final Answer:
- The assertion is **false** and the reason is **true**.