question_answer

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:

\[s=1mm={{10}^{-3}}m,\,\,m=4mg=4\times {{10}^{-3}}g,\] or \[4\times {{10}^{-6}}kg,\,\,u=30m/s,\,\,\,v=0,\,\,\,F=?\] We know F = ma. How to get a? From \[{{v}^{2}}-{{u}^{2}}=2as\] \[\Rightarrow a=\frac{{{V}^{2}}-{{u}^{2}}}{2s}=\frac{{{(30)}^{2}}}{2\times {{10}^{-3}}}=\frac{900}{2\times {{10}^{-3}}}\] \[=4.5\times {{10}^{5}}m/{{s}^{2}}\] \[\therefore \,\,F=4\times {{10}^{-6}}\times 4.5\times {{10}^{5}}=\frac{18}{10}=1.8N\] \[\therefore \]Force exerted by each drop on the head = 1.8N