Classical Mechanics (Kibble & Berkshire) · Problem 10.11
The angular momentum principle — T.W.B. Kibble, F.H. Berkshire
Physics — Mechanics · rocket-motion
Problem
A raindrop falls vertically through stationary mist, collecting mass as it falls. The raindrop remains spherical and the rate of mass accretion is proportional to its speed and the square of its radius. Show that, if the drop starts from rest with a negligible radius, then it has constant acceleration g/7. [Tricky ODE.]