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:
Radius of a raindrop, r = 1 mm = 10⁻³ m
Mass of a raindrop, m = 4 mg = 4 × 10⁻⁶ kg
Distance coved by the drop on the head, s = 10⁻³ m
Initial speed of the drop, v = 0

Final speed of the drop, u = 30 m/s

Using \[a = \frac{v^2 - u^2}{2s}\] , we get:

a = `(- 30)^2/2 xx 10^-3 = 900/2 xx 10^3 = 4.5 xx 10^5` m/s² 

Force, F = ma

⇒ F = 4 × 10⁻⁶ × 4.5 × 10⁵ = 1.8 N