Two particles of masses m 1 and m 2 are initially at rest at an infinite distance apart. If they approach each other under their mutual interaction given by F = - K r 2 . Their speed of approach at the instant when they are at a distance d apart is

Step-by-step solution

Let μ be the reduced mass of the system and v be the approach speed of the particles, then 1 2 μv 2 = ∫ ∞ d F → . d r → ⇒ 1 2 m 1 m 2 m 1 + m 2 v 2 = - ∫ ∞ d K r 2 dr ∴ v = 2 K d 1 m 1 + 1 m 2