Conservation of Momentum of Centre of Mass – Rankers Physics

Motion of Center of Mass: Practice Problem & Solution

Read the statements marked as assertion (A) and reason (R) and choose the correct option. Assertion (A): If no external force acts on a system, the velocity of the centre of mass remains constant. Reason (R): If there is no external force on system, then momentum of system is conserved.  
Both (A) and (R) are true and (R) is the correct explanation of (A)
Both (A) and (R) are true but (R) is not the correct explanation of (A)
(A) is true but (R) is false
(A) is false but (R) is true

Solution Explained:

To solve this problem, we apply the core principles of Motion of Center of Mass. Understanding the underlying formula is key to arriving at the correct answer below:

If the net external force on a system is zero, its linear momentum is conserved (\(vec{P} = M\vec{v}_{\text{cm}} = \text{constant}\)). Consequently, the velocity of the centre of mass \(\vec{v}_{\text{cm}}\) remains constant.

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