Question

if two bodies of equal mass ,initially at r distance , come closer to by virtue of their force of gravitation and do elastic collision what is the maximum distance between the particles if force of gravitation still exists and initially they were at rest ?

Answer 1

Initially, they were at rest. The only force acting between them was the gravitational force. So the total mechanical energy of the system can be considered as only the potential energy due to gravity as the kinetic energy is zero. Finally when they collide and afterwards they are at a maximum distance. Maximum distance implies that they come to rest. Hence their kinetic energy would be zero. They undergo elastic collision so there is no unaccounted non conservative energy. Sine the final and initial mechanical energy must remain the same according to energy conservative. Sine in final and initial cases only the potential energy remains. Hence they must be equal. So the finally, the distance between them remains the same that is 'r'.

Intact, whatever be the mass of the bodies, if conservative force (gravitational here) acts and the bodies undergo elastic collision, the final and initial separation between them remains the same as the law of energy Conservation has to be obeyed.