Motion of the Center of Mass: Let us take the motion of a object of n particles of individual masses m1, m2, ......., mn and net mass M. It is assumed that no mass enters or leaves the object during its motion, so that M remains fixed. Then, as we have seen, we have the relation
Or
Differentiating this expression with related to time t, we have
Since, 
= velocity
Therefore, 
... (i)
Or velocity of the Center of Mass is 
Or 
Further, 
= momentum of a particle 
. Therefore, Eq. (i) can be written as
Differentiating Eq. (i) with related to time t, we get
Or 
... (ii)
Or 
Or 
Further, in accordance with Newton's second law of motion 
. Hence, Eq. (ii) can be written as
Thus, as noticed out earlier also, the centre of mass of a object of particles moves as though it were a particle of mass same to that of the entire system with all the external forces operating directly on it.
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