A rain drop of radius 2mm, falls from a height of 500 m above the ground. It falls with decreasing acceleration due to viscous resistance of air until half its original height. It attains its maximum (terminal ) speed, and moves with uniform speed there after. What is the work done by the gravitational force on the drop in the first half and second half of its journey ? Take density of water `=10^(3)kg//m^(3)`. What is the work done by the resistive force in the entire journey if its speed on reaching the ground is `10ms^(-1)` ?

Explanation

To solve the problem step by step, we will calculate the work done by gravitational force in the first half and second half of the journey of the raindrop, and then determine the work done by the resistive force throughout the entire journey.

### Step 1: Calculate the mass of the raindrop

Given:
- Radius of the raindrop, \( r = 2 \text{ mm} = 2 \times 10^{-3} \text{ m} \)
- Density of water, \( \rho = 10^3 \text{ kg/m}^3 \)

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