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. $m{v}^3$
• B. $\frac{1}{2}m{v}^2$
• C. $\frac{1}{2}{m}^2{v}^2$
• D. $\frac{1}{2}m{v}^3$
• E. $\frac{1}{4}m{v}^3$

Answer 1

Answer: (D)

Velocity of water is $v$, mass flowing per unit length is $m$.
$\therefore$ Mass flowing per second $=mv$
$\therefore$ Rate of kinetic energy or K.E. per second
$=\frac{1}{2}(mv)v^2=\frac{1}{2}m{v}^3$