A bottle has a thin nozzle on top. It is filled with water, held horizontally at a height of 1 m and squeezed slowly by hands so that the water jet coming out of the nozzle hits the ground at a distance of 2m . If the area over which the hands squeeze it is `10 cm^2.` the force applied by hand is close to (take g= 10 `m//s^2` and density of water= 1000 `kg//m^3` )

Options

A. `20 N`
B. `10 N`
C. `5 N`
D. `2.5 N`

Answer

B

Explanation

Apply Bernoulli between point-1 and point-2
` P_1 +1/2 rho V_(1)^(2) = P_2 +1/2 rho V_(2)^(2)`
` P_1 = P_("atm") +("Force by hand ")/( "Area")`
`V_1 ` tends to zero becomes area of point-2 is very small .
` P_2 = P_("atm")`
` P_("atm")+F//A =P_("atm") +(1//2 ) rho V_(2)^(2) implies V_(2)^(2) = (2F )/(PA)`
from kinematics
`2= sqrt((2(h))/(g )xx ) V^2`
` therefore V_(2)^(2) = 20`
using (i) &(ii) we get
`20 = (2F)/(rho A) therefore F=10 N`