Rain Drops falling down in a uniform cloud

Erfan

1. The problem statement, all variables and given/known data
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 [tex]\dot{r}[/tex], velocity of the drop, and the two densities.
(b) Find rain drop's acceleration.
2. Relevant equations



3. The attempt at a solution
The differential equation is non-linear.

chaoseverlasting

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

Erfan

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