JEE Main Physics question
An engine pumps water continuously through a hole. Speed with which water passes through the hole nozzle is v and k is the mass per unit length of the water jet as it leaves the nozzle. Find the rate at which kinetic energy is being imparted to the water.
Answer: (B)
Solution
Mass flowing per unit time, dm/dt = k·v (mass per length × speed). Rate of KE imparted = d/dt(½mv²) = ½v²(dm/dt) = ½v²(kv) = ½kv³.