A rain drop of radius r is falling through air, starting from rest. The work done by all the forces on the drop, by the time it attains terminal velocity, is proportional to

v=2gr2(ρ−σ)9η        Work done by all the forces on the drop = change in its kinetic energy W =12mv2−12mu2=12mv2   [∵u=0]    =12×43πr3.ρ(2gr2(ρ−σ)9η)2 [∵ρ=mV]k=8πρg2(ρ−σ)2r7243η2⇒W=kr7or W∝r7