[QUE/CM-01016]

 Water drop falling through saturated atmosphere.
A spherical  water droplet falls, without friction and under influence of gravity, through an atmosphere   saturated with water vapor. Let its initial radius ($t=0$)  be $c$, its initial velocity, $v_0$. As a result of condensation the  water drop experiences continuous increase in mass proportional to its surface; Show that its radius increases then increases linearly with time. Integrate the differential equation of motion by introducing $r$ instead of $t$ as an independent variable. Show that for $c=0$, the velocity increases linearly with time.

 Source::Sommerfeld