The average mass of rain drops is 3.0 10⁻⁵ ~kg and their avarage 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.

Step-by-step solution

Total volume of rain drops, received 100 ~cm in a year by area 1 ~m ^2 =1 ~m ^2 100 100 ~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 v=10^3 1=10^3 ~kg Average terminal velocity of rain drop v=9 ~m / s (given) Therefore, energy transferred by rain, aligned &E= 1 2 m v^2 &= 1 2 10^3 (9)^2 &= 1 2 10^3 81=4.05 10^4 ~J aligned