Q. 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) $\frac{1}{2}mv^{3}$
B) $mv^{3}$
C) $\frac{1}{2}mv^{2}$
D) $\frac{1}{2}m^{2}v^{2}$
Explanation
(a) $\frac{dk}{dt} = \frac{d}{dt}\left( \frac{1}{2}Mv^{2} \right) = \frac{v^{2}}{2}.\frac{dM}{dt} = \frac{v^{2}}{2}\left( \frac{dM}{dl} \times \frac{dl}{dt} \right)$
$\Rightarrow \frac{dk}{dt} = \frac{1}{2}mv^{2} \times \frac{dl}{dt} = \frac{1}{2}mv^{3}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.