Question

A 1 sq. km area records a rainfall of 25 mm due to 1000 m high clouds. Calculate the work done to raise the water to the height of the clouds. Given g = 10 m/s² . Density of water = 1000 kg m^-3 .

Answer 1

We have area A = 1 sq. km = 1000 m x 1000 m

= 10⁶m²

d = 25 mm = 25 × 10^-3m

Volume of water collected due to rainfall = A.d = 25 × 10³m³

Mass of water = Volume x density

= 25 x 10⁶ kg

Fore applied to raise water = F = mg = 25 x 10⁷ N

Distance moved = h = 1 km = 10³ m

∴ Work done = Fh = 25 × 10⁷ × 10³ = 2.5 x 10¹¹ J