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Assertion:- In two particle system when ...

Assertion:- In two particle system when viewed from center of mass reference frame, if one particle slops then other one will also stop simultaneously, irrespective of external forces acting on system.
Reason:- Centre of mass of a system is a point about which total momentum of system is always constant and non-zero.

A

If both Assertion `&` Reason are True `&` the Reason is a correct explanation of the Assertion.

B

If both Assertion `&` Reason are True but Reason is not a correct explanation of the Assertion.

C

If Assertion is True but the Reason is False.

D

If both Assertion `&` Reason are False.

Text Solution

AI Generated Solution

The correct Answer is:
To analyze the given assertion and reason, we will break down the concepts involved step by step. ### Step 1: Understanding the Assertion The assertion states that in a two-particle system viewed from the center of mass (CM) reference frame, if one particle stops, the other will also stop simultaneously, regardless of external forces acting on the system. **Explanation:** - In the center of mass frame, the velocities of the two particles are measured relative to the center of mass. - If one particle stops (i.e., its velocity relative to the CM becomes zero), the other particle must also have its velocity relative to the CM become zero to maintain the conservation of momentum. ### Step 2: Analyzing the Reason The reason provided states that the center of mass of a system is a point about which the total momentum of the system is always constant and non-zero. **Explanation:** - The center of mass (CM) of a system moves with a velocity that is determined by the total momentum of the system divided by the total mass. - If there are no external forces acting on the system, the momentum of the system is conserved, meaning the velocity of the center of mass remains constant. ### Step 3: Evaluating the Assertion and Reason 1. **Assertion Evaluation:** - If one particle stops in the CM frame, the other must also stop to conserve momentum. This is true. 2. **Reason Evaluation:** - The reason states that the total momentum is always constant and non-zero. This is misleading because while the momentum is conserved in an isolated system, it can be zero if the system is at rest or if the particles are equal and opposite in momentum. Therefore, the reason is false. ### Conclusion - The assertion is true, while the reason is false. Thus, the correct answer is that the assertion is correct, but the reason is incorrect. ### Final Answer - **Assertion:** True - **Reason:** False
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