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 the water?

A. 0.5 v^3 — The rate of kinetic energy is the power. Power is the product of the mass flow rate and the kinetic energy per unit mass.

JEE Main · PhysicsMedium

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

Show correct answer & step-by-step solution

Correct answer: A — $0.5 \lambda v^3$

Mass flow rate

\frac{d m}{d t} = λ v

. Kinetic energy

K = \frac{1}{2} m v^{2}

. Power

P = \frac{d K}{d t} = \frac{1}{2} v^{2} \frac{d m}{d t} = \frac{1}{2} v^{2} (λ v) = 0.5 λ v^{3}