Two masses m1 and m2 are initially at rest and are separated by a very large distance. If the masses approach each other subsequently, due to gravitational attraction between them, their relative velocity of approach at a separatation of d is

As there is no external force acting on the system, linear momentum of the system is conserved.0=m1V1→+m2V2→ magnitude V2=m1V1m2---1the relative velocity of approach is V2→-V1→=V2+V1=m1+m2m2V1----2Applying conservation of mechanical energy for the system0=-Gm1m2d+12m1V12+12m2V22 substituting (1) in the above we get V1=2Gm22m1+m2dSubstitute V1 in (2) we getrelative velocity of approach =2Gm1+m2d