Question

Two bodies of masses m₁ and m₂ are initially at rest at infinite distance apart. They are then allowed to move towards each other under mutual gravitational attraction. Find their relative velocity of approach at a separation distance r between them.

Answer 1

Let v_r be the relative velocity of approach of two bodies at a distance r apart. The reduced mass of the system of two particles is 

According to law of conservation of mechanical energy.

Decrease in potential energy = increase in K.E.