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

Options

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

Answer

B

Explanation

Here, area of cross section of tube
`a_(1)=6 cm^(2)=6xx10^(-4) m^(2)`
Number of holes =50
Diameter of each hole, D=1mm, `10^(-3)`m
Radius of hole, `r=(D)/(2)=(1)/(2)xx10^(-3)=5xx10^(-4)`m
Area of cross-section of each hole
`=pir^(2)=pi(5xx10^(-4))^(2) m^(2)`
Speed of liquid inside the tube,
`v_(1)=1.2 m "min"^(-1)=(1.2)/(60) m s^(-1)=0.02 m s^(-1)`
Let the velocity of ejection of the liquid through the hole `v_(2)`
As `a_(1)v_(1)=a_(2)v_(2)`
or `v_(2)=(a_(1)v_(1))/(a_(2))=(6xx10^(-4)xx0.02)/(50xxpi(5xx10^(-4))^(2))=0.31 m s^(-1)`