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Question
Suppose the average mass of raindrops is 3.0 × 10–5 kg and their average terminal velocity 9 ms–1. Calculate the energy transferred by rain to each square metre of the surface at a place which receives 100 cm of rain in a year.
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Solution
Given, the average mass of raindrops
(m) = 3.0 × 10–5 kg
Average terminal velocity = (V) = 9 m/s
Height (h) = 100 cm = 1 m
Density of water (ρ) = 103 kg/m3
Area of the surface (A) = 1 m2
The volume of the water due to rain (V) = Area × Height
= A × H
= 1 × 1
= 1 m3
Mass of the water due to rain (M) = Volume × Density
= V × ρ
= 1 × 103
= 103 kg
∴ Energy transferred to the surface = `1/2` mv2
= `1/2 xx 10^3 xx (9)^2`
= 40.5 × 103 J
= 4.05 × 104 J
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