A motor engine pumps (1800 ~L ) of water per minute from a well of depth (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 ) )

Step-by-step solution

Given, depth of a well, (d=30 ~m ) water quantity per minute (=1800 ) litre cross-section area of pipe, (A=30 ~cm ^2 ) (=30 10⁻⁴ ~m ^2 ) Now, velocity of water a jet (= 1800 10⁻³ (30 10⁻⁴ ) 60 =10 ~m / s ) and work done by engine (=m g d+ 1 2 m v^2 ) ( aligned & =1800 10 30+ 1 2 1800 (10)^2 & =540000+90000=630000 ~J aligned ) Power of engine, (P= W t = 630000 60 ) (=10500 ~W =10.5 ~kW )