An engine pump is used to pump a liquid of density `rho` continuously through a pipe of cross-sectional area A. If the speed of flow of the liquid in the pipe is v, then the rate at which kinetic energy is being imparted to the liquid is 

Options

A. `1/2 A rho v^3`
B. `1/2 A rho v^2`
C. `1/2 A rho v`
D. `A rho v`

Answer

A

Explanation

Volume flowing/second = Av
Mass flowing/second , `m = A vrho`
Rate at which kinetic energy is imparted to the liquid is
`= 1/2 mv^2 = 1/2 (A vrho) v^2 = 1/2 A rho v^3`.