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

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

(d) Rate of flow of water $\frac{V}{t} = \frac{10\ cm^{3}}{\sec} = 10 \times 10^{- 6}\frac{m^{3}}{\sec}$
Density of water $\rho = \frac{10^{3}kg}{m^{3}}$
Cross-sectional area of pipe $A = \pi\left( 0.5 \times 10^{- 3} \right)^{2}$
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 $F = 0.127\ N$

Dr. Abubacker
Reviewed by Dr. Abubacker

Physics Educator & NEET/JEE Specialist

Ph.D. in Physics with 19+ years of teaching experience.

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