Raindrops, each having a radius of 1 mm and a mass of 4 mg , are...

Given, mass of a raindrop, $m = 4 \text{ mg} = 4 \times 10^{-6} \text{ kg}$

Initial speed of the raindrop, $u = 30 \text{ m/s}$

Final speed of the raindrop, $v = 0 \text{ m/s}$

Distance traveled during impact, $s = r = 1 \text{ mm} = 10^{-3} \text{ m}$

Using the work-energy theorem, the work done by the stopping force equals the change in kinetic energy of the raindrop:

$F \times s = \dfrac{1}{2} m u^2$

$F \times 10^{-3} = \dfrac{1}{2} \times 4 \times 10^{-6} \times (30)^2$

$F \times 10^{-3} = 2 \times 10^{-6} \times 900$

$F \times 10^{-3} = 1.8 \times 10^{-3}$

$F = 1.8 \text{ N}$

By Newton's third law, the force exerted by the drop on the head is equal in magnitude to the stopping force, which is $1.8 \text{ N}$.