Find the limiting velocity of a rain drop assuming diameter of 5.0×10^-4m.The density of air relative to water is 1.3×10^-3

The trick here is guessing the drag coefficient of the raindrop shape.

See:
http://home2.fvcc.edu/~dhicketh/DiffEqns/Spring11projects/Ben_Lynch_Gavin_Lommatsch/DiffEqProject/DiffEqProjectGavinBen.pdf

It is a function of Reynolds number even if the shape is spherical. However using .3 as a guess:

v = sqrt [ 2 m g / (rho A C) ]

here rho = (1.3*10^-3)(1000 kg/m^3)
= 1.3 kg/m^3

m = 1000 *(4/3) pi r^3
m g = 9,800 *(4/3)pi r^3
2 m g = 26.1 *10^3 pi r^3

Rho A C = 1.3 *pi r^2 * .3 = .39 pi r^2
so
v^2 = 26.1 *10^3 pi r^3/(.39 pi r^2)

v^2 = 66.9 *10^3 *2.5*10^-4
v^2 = 16.7
v = 4.1 m/s