Laws Of Motion Question 268
Question: A gardner waters the plants by a pipe of diameter 1mm. The water comes out at the rate or 10 cm3/sec. The reactionary force exerted on the hand of the gardner is [KCET 2000]
Options:
A) Zero
B) $ 1.27\times {{10}^{-2}}N $
C) $ 1.27\times {{10}^{-4}}N $
D) $ 0.127N $
Show Answer
Answer:
Correct Answer: D
Solution:
Rate of flow of water $ \frac{V}{t}=\frac{10cm^{3}}{\sec }=10\times {{10}^{-6}}\frac{m^{3}}{\sec } $
Density of water $ \rho =\frac{10^{3}kg}{m^{3}} $
Cross-sectional area of pipe $ A=\pi {{(0.5\times {{10}^{-3}})}^{2}} $
Forcse $ =m\frac{dv}{dt}=\frac{mv}{t}=\frac{V\rho v}{t}=\frac{\rho V}{t}\times \frac{V}{At}={{( \frac{V}{t} )}^{2}}\frac{\rho }{A} $
$ ( \because \ v=\frac{V}{At} ) $ By substituting the value in the above formula we get $ F=0.127N $
