Question

A gardner waters the plants by a pipe of diameter 1mm. The water comes out at the rate or 10cm³/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. $0.127N$

Answer 1

Answer: (D)

$0.127N$

Answer 2

Rate of flow of water $\frac{V}{t} = \frac{10cm^{3}}{sec^{- 6}\frac{m^{3}}{\sec}}$

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

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

Force$= m\frac{dv}{dt} = \frac{mv}{t} = \frac{V\rho v}{t} = \frac{\rho V}{t} \times \frac{V}{At} = \left( \frac{V}{t} \right)^{2}\frac{\rho}{A}$

$\left( \because\mspace{6mu} v = \frac{V}{At} \right)$

By substituting the value in the above formula we get

$F = 0.127N$