Two bodies of masses (m₁ ) and (m₂ ) initially at rest at infinite distance apart move towards each other under gravitational force of attraction. Their relative velocity of approach when they are separated by a distance (r ) is ( ( G = ) universal gravitational constant.)

Step-by-step solution

Initially when the two masses are at an infinite distance from each other, their gravitational potential energy is zero. When they are at a distance (r ) from each, the gravitational (P E ) is ( PE = -G m₁ m₂ r^2 ) The minus sign-indicates that there is a decrease in PE. This gives rise to an increase in kinetic energy. If (v₁ ) and (v₂ ) are their respective velocities when they are a distance (r ) apart then, from the law of conservation of energy, we have ( 1 2 m₁ v₁^2= G m₁ m₂ r or v₁= 2 G m₂ r ) and ( 1 2 m₂ v