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A cluster of clouds at a height of 1000m...

A cluster of clouds at a height of 1000m above the earth burst and enough rain fell to cover an area of `10^(6)m^(2)` with a depth of 2cm. How much work would have been done in raising water to the height of clouds ? Take `g=10m//s^(2)` and density of water `10^(3)kg//m^(3)`.

Text Solution

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The correct Answer is:
11
Area `A= 10^(6) m^(2)`
Depth, `d= 2cm = 2 xx 10^(-2)m`
`therefore` Volume of water
`= A d = 10^(6) xx 2 xx 10^(-2) = 2 xx 10^(4) m^(3)`
Mass of water, m= Volume `xx` density
`=2 xx 10^(4) xx 10^(3)= 2 xx 10^(7) kg`
Force used in raising water to the height of clouds, F= Weight of water `=mg = 2 xx 10^(7) xx 9.8N`
Work done, `W= Fs= 2 xx 10^(7) xx 9.8 xx 1000= 1.96 xx 10^(11)J`
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