Work Energy And Power Question 202
Question: An engine pump is used to pump a liquid of density $ \rho $ continuously through a pipe of cross-sectional area A. If the speed of flow of the liquid in the pipe is v, then the rate at which kinetic energy is being imparted to the liquid is
Options:
A) $ \frac{1}{2}A\rho v^{3} $
B) $ \frac{1}{2}A\rho v^{2} $
C) $ \frac{1}{2}A\rho v $
D) $ A\rho v $
Show Answer
Answer:
Correct Answer: A
Solution:
Energy supplied to liquid per second by the pump = $ \frac{1}{2}\frac{mv^{2}}{t} $ = $ \frac{1}{2}\frac{V\rho v^{2}}{t} $ = $ \frac{1}{2}A\times ( \frac{l}{t} )\times \rho \times v^{2} $
$ [ \frac{l}{t}=v ] $
$ =\frac{1}{2}A\times v\times \rho \times v^{2} $ = $ \frac{1}{2}A\rho v^{3} $
