A water droplet falling in the atmosphere is spherical. Assume that as the droplet passes through a cloud, it acquires mass at a rate equal to kA where k is a constant (>0) and A its cross-sectional area. Consider a droplet of initial radius r0 that enters cloud with a velocity v0. Assume no resistive force and show
(a) That the radius increases linearly with the time, and
(b) That if r0 is negligibly small then the speed increase linearly with the time within the cloud.