Question

An engine pumps water continuously through a hose. Water leaves the hose with a velocity v and m is the mass per unit length of the water jet. What is the rate at which kinetic energy is imparted to water :

• A. $\frac{1}{2}{m}^2{v}^2$
• B. $\frac{1}{2}m{v}^2$
• C. $\frac{m{v}^3}{2}$
• D. $\frac{1}{6}{m}^2{v}^2$

Answer 1

The correct option is C $\frac{m{v}^3}{2}$

Let $m$ is the mass per unit length rate of mass per $sec$ = $mx/t=mv$

Rate of $KE=\left(mv\right)v^2/2=m{v}^3/2.$

$=\frac{m{v}^3}{2}$

Hence,

option $\left(C\right)$ is correct answer.