# Rain Drops falling down in a uniform cloud

## Homework Statement

Consider a uniforms cloud of density ρ1 which consists of many little drops that are approximately still.Consider a special rain drop that is a little more bigger than the others so that it starts to fall down.Water drops stays spherical all the way.But the radius gets higher as it falls down.Also water's density is ρ0.
(a) Find a relation between $$\dot{r}$$, velocity of the drop, and the two densities.
(b) Find rain drop's acceleration.

## The Attempt at a Solution

The differential equation is non-linear.

## Answers and Replies

Any thoughts on how to go about this? Any logical assumptions?

We have no air resistance force.But it might be possible to find a solution when the air exerts linear resistance force.