question_answer 13)

A rain drop of radius 2 mm falls from a height of 500 m above the ground. It falls with decreasing acceleration (due to viscous resistance of the air) until at half its original height, it attains its maximum (terminal) speed and moves with uniform speed thereafter. What is the work done by the gravitational force on the drop in the first and second half of its journey ? What is the work done by the resistive force in the entire journey if its speed on reaching the ground is ?  

Answer:

Whether the rain drop falls with decreasing acceleration or with uniform speed, the work done by gravitational force on the drop remains same. Here r = 2 mm Distance moved in each half journey,                  Density of water,   Mass of rain drop, m = Volume  density   Work done by the gravitational force on the rain drop in each journey, . For entire journey, Work done by gravitational force + Work done by resistive force = Gain in K.E.   or