An engine pumps liquid of density d continuosly through a pipe of cross-section are A. If the speed with which liquid passes through the pipe is v, then the rate at which kinetic energy is being imparted to the liquid by the pump is

Options

A. `(1)/(2)Arhov^(3)`
B. `(1)/(Arhov^(2)`
C. `(1)/(2)Arhov`
D. `Arhov`

Answer

A

Explanation

Energy supplied to liquid per second by the pump
`=(1)/(2) (mv^(2))/(t)= (1)/(2) (V rho v^(2))/(t) = (1)/(2) A xx ((l)/(t))xx rho xx v^(2) [(l)/(t) =v]`
`=(1)/(2)A xx v xx rho xx v^(2) = (1)/(2) A rho v^(3)`