The cylindrical tube of a spary pump has a cross-section of `6 cm^(2)` one of which has 50 holes each of diameter `1mm`. If the liquid flow inside the tube is `1.2m` per minutes, then the speed of ejection of the liquid through the holes is

Options

A. `2.1ms^(-1)`
B. `0.31 ms^(-1)`
C. `0.96 ms^(-1)`
D. `3.4 ms^(-1)`

Answer

B

Explanation

Here, area of cross section of tube
`a_(1) = 6 cm^(2) = 6 xx 10^(-4) m^(2)`
Number of holes = 50
Diameter of each holes, `D = 1 mm = 10^(-3)m`
Radius of hole, `r= D/2 = 1/2 xx 10^(-3) = 5 xx 10^(-4)m`
Area of cross-sectional of each hole
`=pir^() = pi(5xx10^(-4))^(2)m^(2)`
Total area of cross-section of 50 holes.
`a_(2) = 50 xx pi (5 xx 10^(-4))^(2)m^(2)`
Speed of liquid inside the tube,
`v_(1) = 1.2 m min^(-1)`
`=1.2/60 ms^(-1) = 0.02 ms^(-1)`
Let the velocity of ejection of the liquid through hole `v_(2)`
As `a_(1)v_(1) = a_(2)v_(2) `
`or v_(2) = (a_(1)v_(1))/(a_2) = (6 xx 10^(-4) xx 0.02)/(50 xx pi(5 xx 10^(-4))^(2)) = 0.31 ms^(-1)`.