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 $



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