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

Answer

C

Explanation

Mass of liquid flowing out per second m = volume x density
`m=(A v)xxd, K.E. =(1)/(2)mv^(2)`
`K.E. =(1)/(2)(A v d)xxv^(2) =(1)/(2)A d v^(3)`