A motor pump a liquid of density `rho` through a pipe of cross-sectional area A. If the liquid moves with a speed v in this pipe, then the rate of kinetic energy imparted to the liquid is proportional to

Options

A. ` v^(2)`
B. `v^(3)`
C. `v^(4)`
D. `sqrt(v)`

Answer

B

Explanation

`because` Mass flow of rate, `(dm)/(dt)=rhoAv`
Here, A = cross sectional area of pipe,
`rho=` density of liquid
and v = speed of the liquid
`because " Force "F=ma=m(dv)/(dt)=v(dm)/(dt)=v(rhoAv)`
`because KE " "P=F*v=rhoAv^(3)`
Rate of change `KE=(dk)/(dt)=(domega)/(dt)=p`
where, `" "` P = power
and `" "` P = Fv
or `" "P propto v^(3)`