Question

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

• A. $0$ N
• B. $1.27\times {10}^{-2}N$
• C. $1.27\times {10}^{-4}N$
• D. $0.127N$

Answer 1

The correct option is D $0.127N$

reaction force = $A{v}^{2}p$

$F=v\frac{dm}{dt}$

where $v$is the velocity of water

$\frac{dm}{dt}$ is the rate of mass flow

$F=v\frac{dm}{dt}=vp\frac{dv}{dt}$ where$p$ is the density

A= area of cross section then $F=vpA\frac{dv}{dt}=pA{v}^2$

in this question directly $\frac{dv}{dt}$ is given

$\frac{dv}{dt}=Av$

$10=\frac{\pi d^2}{4}v$

therefore $v=\frac{40}{\pi d^2}$

now $F=\frac{40}{\pi d^2}p10$ = $\frac{400\times 1\times 7}{22\times {10}^{-2}}$ = $127.27\times {10}^{-2}$dyne

1dyne = ${10}^{-5}$N

now $F=\frac{127.27}{{10}^{-2}}\times {10}^{-5}=0.127N$

option is D