Question

Show that in the absence of any external force the velocity of center of mass remains constant

Answer 1

Force = rate of change of momentum
Thus when f is zero (i.e.) external force is zero
0=mv-mu/t
0=d(mv) / dt
since m is constant

0=m(dv/dt)
0=dv/dt #

it is constant

Answer 2

Hello there,

Before going to the answer some points are to be considered.

1.force =rate of change of momentum=d(p)/d(t).
2. If an no external force is present, F=0.
3.the fact that mass ≠0.

Coming to the answer.....
F=d(p)/d(t).

We know that p=mv. Where m is mass nd v is velocity.

So F=d(mv)/d(t).

F=m d(v)/d(t).

Since there is no force ,f=0.

So m d(v)/d(t)=0

Mass can never be zero so

So this itself is a self explanatory fact that velocity tends to be constant in such cases.

I hope this helps u .....nd doubts are indeed welcome