A motor engine pumps 1800 L of water per minute from a well dpth 30 m and allows to pass through a pipe of cross-sectional area `30 cm^2`. Then the power of the engine is (Acceleration due to gravity, `g=10 ms^-2`)

Options

A. 20.5 kW
B. 15.5 kW
C. 10.5 kW
D. 9.5 kW

Explanation

Given,
Depth of a well d=30 m
water quantity per minute=1800 litre
cross- section area of pipe, `A=30 cm^2`
`=30 times 10^-4 m^2`
Now,
velocity of water a jet `=(1800 times10^-3)/((30 times10^-4) times60 )=10m//s`
and work done by engine `=mgd+1/2mv^2`
`=1800 times10times30+1/2times1800times(10)^2`
`=540000+90000=630000 J`
Power of engine, `P=W/t=630000/60`
`=10500 W=10.5 k W`