An electric pump is used to pump water to fill a water tank of volume `30m^(3)` in 20 minute. The pump is on the ground floor and the tank is one the terrace of the building. The centre of the tank is at 400 m above the ground. How much electric power is consumed by the pump, in filling the tank, if the efficiency of the pump is 50%?
`(g=10m//s^(2)` and density of water `=10^(3)kg//m^(3)`)

Options

A. 100kW
B. 125kW
C. 150kW
D. 200kW

Answer

D

Explanation

Power `=("Work")/("Time")" " therefore W = P xx t` and `P=(3t^(2))/(2)`
From work energy theorem,
Change in K.E. = Work done = Pdt
`therefore K_(f)-K_(i)= int P dt = int ((3)/(2)t^(2))dt`
`therefore (1)/(2)mv^(2)-0 = int_(0)^(2)((3)/(2)t^(2))dt`
`therefore (1)/(2)(2)v^(2)=[(3)/(2)xx(t^(3))/(3)]_(0)^(2)=[(3)/(2)xx(8)/(3)]=4`
`therefore v^(2)=4` or v = 2 m/s