(a) Show that the velocity of the centre of mass of a moving isolated system remains constant.

Explanation

The equation of motion of a system of particles is given by `M(d^(2)vecr)/(dt^(2))= vecF_(ext)`, where M is the total mass of the system concentrated at the C.M. with position vector `vecr` `Md/(dt)(dvecr)/(dt) = vecF_(ext) rArr M d/(dt)(vecv_(cm))=(dvecr)/(dt)` = velocity of C.M.
Foran isolated system, no external forces acts from outside and all internal forces cancel out in pairs.
`therefore vecF_(ext)=0 therefore M(vecdV_(cm))=0 therefore d/(dt)(vecV_(cm)) = 0 rArr vecV_(cm)` = constant.
The C.M. of an isolated system moves with a constant velocity in a straight line.