A gardener water the plants by a pipe of dimeter `1mm` . The water comes out at the rate or `10cm^(3)//sec` . The reactionary force exerted on the hand of the gardener is

Options

A. Zero
B. `1.27 xx 10^(-2)`N
C. `1.27 xx 10^(-4)N`
D. `0.127N`

Answer

D

Explanation

Rate of flow of water `= ("Volume")/(t) = 10 xx 10^(-6) m^(3)//sec`
Density of water `(p_(w)) = 1000 kg //m^(3)`
Area (A) ` = pi r^(2) = pi (0.5 xx 10^(-3))^(2)`
Force (F) ` = (dv)/(dt) = (mv)/(t) = (V rho v)/(t)`
` = ((V)/(t)) rho v = ((V)/(t)) rho ((V)/(At)) ["Since", v = ("distance")/("time") = (V)/(At) = (AI)/(At)]`
`((V)/(t))^(2) (rho)/(A) = (10 xx 10^(-6))^(2) xx (1000)/(pi xx (0.5 xx 10^(-3))^(-2))`
` = (100 xx 1000 xx 10^(-12))/(pi xx 25 xx 10^(-8))`
` = (10^(-7) xx 10^(-8))/(25pi) = (10)/(25pi) = 0.127N`