A light string passing over a smooth pulley holds two identical buckets at its ends. Mass of each empty bucket is M and each of them holds M mass of sand. The system was in equilibrium when a small leak developed in bucket B (take this time as t = 0). The sand leaves the bucket at a constant rate of `mu` kg/s. Assume that the leaving sand particles have no relative speed with respect to the bucket (it means that there is no impulsive force on the bucket like leaving exhaust gases exert on a rocket). Find the speed `(V_(0))` of the two bucket when B is just empty.

Answer

`V_(0) = (Mg)/(mu) [4ln((4)/(3)) - 1]`