Work Energy and Power - Result Question 39
42. An engine pumps water through a hose pipe. Water passes through the pipe and leaves it with a velocity of $2 m / s$. The mass per unit length of water in the pipe is $100 kg / m$. What is the power of the engine?
(a) $400 W$
(b) $200 W$
(c) $100 W$
(d) $800 W$
[2010]
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Answer:
Correct Answer: 42. (d)
Solution:
(d) Amount of water flowing per second from the pipe
$ =\frac{m}{\text{ time }}=\frac{m}{\ell} \cdot \frac{\ell}{t}=(\frac{m}{\ell}) v $
Power $=$ K.E. of water flowing per second
$=\frac{1}{2}(\frac{m}{\ell}) v \cdot v^{2}$
$=\frac{1}{2}(\frac{m}{\ell}) v^{3}$
$=\frac{1}{2} \times 100 \times 8=400 W$
