A pump on the ground floor of a building can pump up water to fill the tank of 30 ~m ³ in 15 ~min . If the tank is 40 ~m above the ground, and the efficiency of the pump is 30 % , the power consumed by the pump is (g=10 ~ms ⁻² )

Step-by-step solution

Volume of water in tank, V=30 ~m ³ Time taken to fill the tank, t=15 ~min =15 60=900 ~s Height of the tank, h=40 ~m Mass of pumped water, m= Volume Density of water =30 10³=3 10⁴ ~kg Work done by the pump to fill the tank, aligned W &=m g h &=3 10⁴ 10 40 &=1.2 10⁷ ~J aligned Output power of the pump, P_ o = W t = 1.2 10⁷ 900 = 4 3 10⁴ ~W aligned & As we know, efficiency = Output power (P_ o ) Input power (P_ i ) & 0.3= 4 / 3 10⁴ P_ i & P_ i = 4 10⁴ 3 0.3 =4.4 10⁴ ~W =44 ~kW aligned