Two masses `m_(1)` and `m_(2)` at an infinite distance from each other are initially at rest, start interacting gravitationally. Find their velocity of approach when they are at a distance `r` apart.

Explanation

Reduced mass `mu=(m_(1)m_(2))/(m_(1)+m_(2))`
`U_(1)=0, U_(2)=(Gm_(1)m_(2))/r`
If `v` velocity of approach
`1/2muv^(2)=(Gm_(1)m_(2))/r` (`mu`:rediced mass)
`1/2.(m_(1)m_(2))/(m_(1)+m_(2))v^(2)=(Gm_(1)m_(2))/r`
`v^(2)=(2G(m_(1)+m_(2)))/r`
`v=sqrt((2G(m_(1)+m_(2)))/r)`