An engine pumps water continously through a hole. Peeds with which water pases 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 eing imparted to the water.

Options

A. `1/2 kv^2`
B. `1/2 kv^3`
C. `(v^2)/(2k)`
D. `(v^3)/(2k)`

Answer

B

Explanation

`k = ("Mass")/("Length") = (dm)/(dx), v` = speed of water `implies K.E. = 1/2mv^2`
`implies d/(dt) (K.E.) = 1/2 ((dm)/(dt))v^2 = 1/2 ((dm)/(dx) cdot (dx)/(dt)) v^2 = 1/2 kvv^2 = (kv^3)/2`.