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
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4727:Diamond Point