Question

A gardner watering the plants by a pipe of diameter 2 mm. The water comes out at the rate of $10c{m}^3/sec$. The reactionary force exerted on the hand of the gardner is

• A. 0.031 N
• B. 2N
• C. 2.9 N
• D. 4 N

Answer 1

Answer: (A)

(V) Rate of flow $=\frac{V}{t}=\frac{\text{ volume }}{\text{ time }}$
$=\frac{10\times 10^{-6}}{1}=10^{-5}$
Force exerted on the hand of gardener
$=\frac{P}{t}=\frac{mv}{t}$
Area of cross section $=\frac{\pi D^2}{4}=\frac{3.14\times {\left(2\times 10^{-3}\right)}^2}{4}$
$=\frac{3.14\times 4\times 10^{-6}}{4}$
$=3.14\times 10^{-6}$
Area $\times$ velocity $=$ rate of flow
$v=\frac{V}{tA}$
Force $=\frac{mv}{t}=\frac{\rho Vv}{t}=\frac{\rho }{A}{\left(\frac{V}{t}\right)}^2$
$F=\frac{10^3}{3.14\times 10^{-6}}\times {\left(10^{-5}\right)}^2=0.031$
$F=0.031N$