A gardner waters the plants by a pipe of diameter $1\,mm.$ The water comes out at the rate or $10 \,cm^3/sec$. The reactionary force exerted on the hand of the gardner is
A gardner waters the plants by a pipe of diameter $1\,mm.$ The water comes out at the rate or $10 \,cm^3/sec$. The reactionary force exerted on the hand of the gardner is
$Zero$
$1.27 \times {10^{ - 2}}N$
$1.27 \times {10^{ - 4}}\,N$
$0.127\,N$
A gardner waters the plants by a pipe of diameter $1\,mm.$ The water comes out at the rate or $10 \,cm^3/sec$. The reactionary force exerted on the hand of the gardner is
Rate of flow of water $\frac{V}{t} = \frac{{10\,c{m^3}}}{{\sec }} = 10 \times {10^{ - 6}}\frac{{{m^3}}}{{\sec }}$
Density of water $\rho = \frac{{{{10}^3}kg}}{{{m^3}}}$
Cross-sectional area of pipe $A = \pi {(0.5 \times {10^{ - 3}})^2}$
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}$
By substituting the value in the above formula we get $F = 0.127\,N$