Hello,

Suppose there's a spherical solid of initial radius . This solid when dropped in a certain liquid dissolves at the rate . By rate of dissolution I mean the loss of the volume of the solid in unit time. By using derivatives, we can represent it as-

where is change in volume, which is directly proportional to the cube of the change in radius of the spherical solid represented as .

Since the solid moves downward it experiences drag. By Stoke's Law, drag is -

where is the dynamic viscosity of the liquid, is the solid's downward velocity.

But, here downward velocity of the solid is a function of the drag force, which is again a function of the radius.

If we apply Newton's Laws,

where is the solid's mass.

But mass also depends upon radius.

All the variables seem inter-related. I want to reduce the whole situation into an equation but cannot proceed beyond this.

Please suggest what and how to proceed.

**Edited by Sriman Dutta, 28 December 2016 - 04:49 PM.**