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. ` 5.0 xx 10 ^(-3) m `
B. ` 7.5 xx 10 ^(-3 ) m `
C. `9.6 xx 10 ^(-3) m `
D. `3.6 xx 10 ^(-3 ) m `

Answer

D

Explanation

After coming out from tap the water will move under gravity. Let the velocity at a distance h from tap be `v_(2)`.
Using, `v_(2)^(2)=v_(1)^(2)+2gh,"Here"" "v_(1)=0.4ms^(-1) and h=0.2m`
`Rightarrow" "v_(2)sqrt(v_(1)^(2)+2gh)=sqrt((0.4)^(2)+2xx10xx0.2)=2ms^(-1)`
`therefore` According to equation of continuity at section (I) and section (II)
`a_(1)v_(1)=a_(2)v_(2)Rightarrowpi((d_1)/(2))^(2)v_(1)=pi((d_2)/(2))^(2)v_(2)`
Here, `d_(1)=8xx10^(-3)m," "pixx((8xx10^(-3))/(2))^(2)xx0.4=pixx((d_2)/(2))^(2)xx2" "Rightarrow" "d_(2)=3.6xx10^(-3)m`