Water from a tap emerges vertically downwards with an initial spped of `1.0ms^-1`. The cross-sectional area of the tap is `10^-4m^2`. Assume that the pressure is constant throughout the stream of water, and that the flow is steady. The cross-sectional area of the stream 0.15 m below the tap is

Options

A. ` 5.0 xx 10 ^(-4) m ^ 2 `
B. `1.0 xx 10 ^(-5) m ^ 2 `
C. `5.0 xx 10 ^(-5) m ^ 2 `
D. `2.0 xx 10 ^(-5) m ^ 2 `

Answer

C

Explanation

By equation of continuity, `v_(1)A_(1)=v_(2)A_(2)`
`v_(2)`=Velocity of water stream at 0.15m below the tap.
Now `v_(2)^(2)=u^(2)+2aS=v_(1)^(2)+2aS" "or" "v_(2)^(2)=(1)^(2)+2xx10xx0.15=4" "or" "v_(2)=2m//s`
`therefore" "A_(2)=(v_(1)A_(1))/(v_2)=(1xx10^(-4))/(2)=5xx10^(-5)m^(2)" "therefore" ""Cross-sectional area of stream"=5xx10^(-5)m^(2)`