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Water from a tap emerges vertically down...

Water from a tap emerges vertically downwards with an initial speed 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

A

`5.0 xx 10^(-4)m^(2)`

B

`1.0 xx 10^(-4) m^(2)`

C

`5.0 xx 10^(-5)m^(2)`

D

`2.0 xx 10^(-5)m^(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
From conservation of energy
`v_(2)^(2)=v_(1)^(2)+2gh` …(i)
[ can also be found by applying Bernouli's theorem]
From continuity equation
`A_(1)v_(1)=A_(2)v_(2)`

Substituting value of `v_(2)` from Eq. (ii) in eq. (i).
`(A_(1)^(2))/(A_(2)^(2))*v_(1)^(2)=v_(1)^(2)+2gh`
or, `A_(2)^(2)(A_(1)^(2)v_(1)^(2))/(v_(1)^(2)+2gh)`
`:. A_(2)=(A_(1)v_(1))/(sqrt(v_(1)^(2)+2gh))`
Substituting the given values, we get
`A_(2)=((10^4)(1.0))/(sqrt((1.0)^(2)+2(10)(0.15)))`
`A_(2)=5.0xx10^(-5)m^(2)`
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