Two Particle System in CM Frame – Rankers Physics
Topic: Center of Mass , Momentum and Collision
Subtopic: Calculation of Center of Mass

Two Particle System in CM Frame

Assertion (A): In two particle system when viewed from center of mass reference frame, if one particle stops then other one will also stop simultaneously, irrespective of external forces acting on system.
Reason (R): Centre of mass of a system is a point about which total momentum of system is always constant and non-zero.
 
Both (A) & (R) are true and the (R) is the correct explanation of the (A)
Both (A) & (R) are true but the (R) is not the correct explanation of the (A)
(A) is true but (R) is false
Both (A) and (R) are false

Solution:

Assertion (A) is true.

In the center of mass (CM) frame, the total momentum of the system is always zero. If \(p_1 + p_2 = 0\), then \(p_1 = -p_2\). If \(p_1 = 0\), then \(p_2\) must also be zero.

Reason (R) is false; total momentum of the system about the center of mass is always zero, not 'constant and non-zero'.

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