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Show that in absence of any external for...

Show that in absence of any external force the centre of mass of two moving particles moves with uniform velocity.

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If no external force is applied on the particles the resultant momentum of the particles remains conserved. That means, on the above example, `m(vecv_(1)+vecv_(2))` = constant. Clearly both the velocities `vecv_(1) "and" vecv_(2)` can be changed in such a way that the above condition is not violated. On the other hand for the centre of mass of the two particles, 2 `mvecv= m (vecv_(1)+vecv_(2))` =constant.
As mass m is constant, so `vecv` = constant Hence, in absence of any external force the centre of mass of two moving particles moves with uniform velocity.
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