Assertion : The total momentum of an isolated system of particles is conserved.
Reason: The law of conservation of momentum follows from the second and third law of motion.

Options

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

Answer

To solve the question, we need to analyze both the assertion and the reason provided, and determine their validity.

### Step 1: Analyze the Assertion
**Assertion:** The total momentum of an isolated system of particles is conserved.

- An isolated system is defined as one where no external forces act on the particles within the system.
- According to Newton's first law of motion, if no external force acts on a body, it will remain at rest or continue to move at a constant velocity.
- From Newton's second law, we know that the change in momentum of an object is equal to the net external force acting on it multiplied by the time duration of that force. If the net external force is zero, the change in momentum is also zero.
- Therefore, the total momentum of the system remains constant over time, confirming that momentum is conserved in an isolated system.

**Conclusion for Assertion:** The assertion is true.

### Step 2: Analyze the Reason
**Reason:** The law of conservation of momentum follows from the second and third law of motion.

- The second law of motion states that \( F = ma \) (force equals mass times acceleration), which implies that if there is no net force acting on a system, the momentum of the system remains constant.
- The third law of motion states that for every action, there is an equal and opposite reaction. This means that when two particles interact, the forces they exert on each other are equal in magnitude and opposite in direction, which contributes to the conservation of momentum in a closed system.
- However, while the second and third laws support the concept of momentum conservation, the law of conservation of momentum is more directly derived from the first law of motion, which states that in the absence of external forces, the momentum of a system remains constant.

**Conclusion for Reason:** The reason is true but does not correctly explain the assertion, as the law of conservation of momentum is primarily derived from the first law of motion.

### Final Conclusion
- Both the assertion and the reason are true, but the reason is not a correct explanation of the assertion. Therefore, the answer is that both statements are true, but the reason does not correctly explain the assertion.