Ncert Exercises & Solutions

Q.40 Suppose the average mass of raindrops is 3.0 x $10^{- 5}$ kg and their average terminal velocity 9 m/s. Calculate the energy transferred by rain to each square metre of the surface at a place that receives 100 cm of rain in a year.

Hint: Apply energy conservation.

Step 1: Find mass of the water collected per year due to rain.

Given, average mass of raindrop, m $= 3 .0 \times 10^{- 5} kg$
Average terminal velocity, $v_{t}$ = 9 m/s.
Height (h) = 100 cm = 1m
Density of water $(ρ) = 10^{3} kg / m^{3}$
Area of the surface (A) = 1 $m^{2}$
Volume of the water due to rain, V = Area x height
$\begin{array}{l} = A \times h \\ = 1 \times 1 = 1 m^{3} \end{array}$

Mass of the water due to rain (M) = Volume x density

$\begin{array}{l} = V \times ρ \\ = 1 \times 10^{3} \\ = 10^{3} kg \end{array}$

Step 2: Apply energy conservation and find energy transferred per year.

$\begin{array}{l} ∴ Energy transferred to the surface = \frac{1}{2} {mv}^{2} \\ = \frac{1}{2} \times 10^{3} \times (9)^{2} \\ = 40 .5 \times 10^{3} \cdot J = 4 .05 \times 10^{4} J \end{array}$

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