Water is flowing continuously from a tap having an internal diameter `8xx10^(-3)`m. The water velocity as it leves the tap is `0.4 ms^(-1)`. The diameter of the water stream at a distance `2xx10^(-1)`m below the tap is close to `(g=10m//s^(2))`

Options

A. `7.5xx10^(-3)m`
B. `9.6xx10^(-3)m`
C. `3.6xx10^(-3)m`
D. `5.0xx10^(-3)m`

Answer

C

Explanation

Velocity of stream at 0.2 m below tap
`v_(2)^(2) =v_(1)^(2) +2as =(0.4)^(2) +2xx10xx0.2=4.16`
or `v_(2) =sqrt(4.16) =2.04m//s =2 m//s ~~ 2m//s`
Ac cording to equation of continuity
`A_(1)v_(1) =A_(2)v_(2)` or `pi r_(1)^(2)v_(1) =pi r_(2)^(2)v_(2)`
or `r_(2)= sqrt((r_(1)^(2)v_(1))/(v_(2))) =sqrt(((4xx10^(-3))^(2)xx0.4)/(2))`
`~~1.8xx10^(-3)m`
Diameter of the water stream
`=2 r_(2) =2xx1.8xx10^(-3)m =3.6xx10^(-3)m`