Question

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.

Answer 1

Correct Answer - A::B
Let `nu_(r)` be their velocity of approach. From conservation of energy,
Increase in kinetic energy
`=` decrease in gravitational potential energy
or `(1)/(2) mu nu_(r)^(2) = (Gm_(1)m_(2))/(r)` ..(i)
Here, `mu =` reduced mass
`= (m_(1)m_(2))/(m_(1) + m_(2))`
Subsituting in Eq.(i), we get
`nu_(r) = sqrt((2G(m_(1) + m_(2)))/(r))`