Physics - W.E.P. Question with Solution | TestHub

The volume of water flowing per unit time is $Av$. The mass of water lifted per unit time is $dm/dt=\rho Av$. Thus, A is correct. The rate at which potential energy is gained is $(dm/dt)gh=\rho Avgh$. Thus, B is correct. The rate at which kinetic energy is gained is $\frac{1}{2}(dm/dt)v^2=\frac{1}{2}(\rho Av)v^2=\frac{1}{2}\rho A{v}^3$. Thus, C is correct. The minimum power required by the pump is the sum of the rates of change of potential and kinetic energy, which is $P=\rho Avgh+\frac{1}{2}\rho A{v}^3=\rho Av(gh+\frac{1}{2}{v}^2)$. Thus, D is correct.