Consider the following two statements:

(A) Linear momentum of the system remains constant.


(B) Centre of mass of the system remains at rest.


We know that,


So, Centre of mass at rest means v(cm)=0, hence, linear momentum of the system must be zero.


So, B implies A. Now, Linear momentum constant means, it may be other than zero, and in that


case velocity of centre of mass will be non-zero too. Hence, A doesn’t imply B.

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