Question

A gardener waters the plants by a pipe of diameter $1mm$ The water comes out at the rate or $10c{m}^3/sec$. The reactionary force exerted on the hand of the gardener is

• A. Zero
• B. $1.27\times 10^{-2}N$
• C. $1.27\times 10^{-4}N$
• D. $0.127N$

Answer 1

Answer: (D)

Rate of flow of water $\frac{V}{t}=\frac{10c{m}^2}{sec}$

$=10\times 10^{-6}\frac{m^3}{sec}$

Density of water $\rho =\frac{10^{3}kg}{m^3}$

Cross-sectional area of pipe $A=\pi (0.5\times 10^{-3}{)}^2$

Force $=m\frac{dv}{dt}=\frac{mv}{t}$

$=\frac{V\rho v}{t}=\frac{\rho V}{t}\times \frac{V}{At}$

$={\left(\frac{V}{t}\right)}^2\frac{\rho }{A}\left(\because v=\frac{V}{At}\right)$

By substituting the value in the above formula we get

$F=0.127N$