The cylindrical tube of a spray pump has a cross-section of `8 cm^(2)`, one end of which has 40 fine holes each of area `10^(-8) m^(2)`.If the liquid flows inside the tube with a speed of `0.15 m m^(-1)`, the speed with which the liquid is ejected through the holes is

Options

A. `50 ms^(-1)`
B. `5 ms^(-1)`
C. `0.05 ms^(-1)`
D. `0.5 ms^(-1)`

Answer

B

Explanation

According to equation of continuity, (area a) xx (velocity v) = constant.
`therefore` For tube,`(8 xx 10^(-4))xx ((0.15)/(60)) = a_(1)v_(1)`
`therefore` For holes, `(40 xx 10^(-8)) xx v = a_(2)v_(2)`
`therefore a_(2)v_(2) = a_(1)v_(1)`
`therefore 40 xx 10^(-8) xx v = (8 xx 10^(-4)xx0.15)/(60)`
or `v = (8 xx 10^(-4) xx 0.15)/(40 xx 10^(-8) xx 60) = (8 xx 15)/(4xx6) = 5 ms^(-1)`