Rain Drops falling down in a uniform cloud

[Erfan]

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.

Homework Equations

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.