The average mass of rain drops is $$3.0 \times {10^{ - 5}}kg$$   and their average terminal velocity is $$9\,m/s.$$  Calculate the energy transferred by rain to each square metre of the surface at a place which receives $$100\,cm$$  of rain in a year.

Solution :
Total volume of rain drops, received $$100\,cm$$  in a year by area $$1\,{m^2}$$
$$ = 1\,{m^2} \times \frac{{100}}{{100}}m = 1\,{m^3}$$
As we know, density of water,
$$d = {10^3}kg/{m^3}$$
Therefore, mass of this volume of water
$$M = d \times v = {10^3} \times 1 = {10^3}kg$$
Average terminal velocity of rain drop
$$v = 9\,m/s\left( {{\text{given}}} \right)$$
Therefore, energy transferred by rain,
$$\eqalign{ & E = \frac{1}{2}m{v^2} = \frac{1}{2} \times {10^3} \times {\left( 9 \right)^2} = \frac{1}{2} \times {10^3} \times 81 \cr & = 4.05 \times {10^4}J \cr} $$