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

Step-by-step solution

Given, radius of rain drop (= r ) Since, rain drop starts falling from rest, hence its initial speed, (u= 0 ) Final velocity of rain drop is equal to the terminal velocity (v ), which is given by (v= 2 g r^2( - ) 9 ) where, ( ) density of the rain drop ( ) density of air ( ) coefficient of viscosity ( ) According to the work-energy theorem, work done by all the forces on the drop = change in its kinetic energy ( array rlr W & = 1 2 m v^2- 1 2 m u^2= 1 2 m v^2 & [ u=0] & = 1 2 4 3 r^3 ( 2 g r^2( - ) 9 )^2 & [ = m V