Question

Raindrops of radius 1 mm and mass 4 mg are falling with a speed of 30 m/s on the head of a bald person. The drops splash on the head and come to rest. Assuming equivalently that the drops cover a distance equal to their radii on the head, estimate the force exerted by each drop on the head.

Answer 1

Given, r = 1 mm = ${10}^{-3}m,$

m = 4 mg = $4\times {10}^{-6}kg$

S = ${10}^{-3}m,$

V = 0, u = 30 m/s

We know, $a=\frac{v^2-u^2}{2\times {10}^{-3}}=\frac{-30\times 30}{2\times {10}^{-3}}$

=$-4.5\times {10}^{5}m{s}^{-2}$ (decelerating)

Taking magnitude only,

deceleration = $4.5\times 10m/s^2$

$\therefore$ Force , F = $4\times {10}^{-6}\times 4.5\times {10}^5$

= 1.8 N