# Water from a tap emerges vertically downwards with an initial speed of $1.0ms^{-1}$ The cross -sectional area of the tap is $10^{-4}m^{2}$ .Assume that that the pressure is constant throughout the stream of water and that the flow is streamlined. The cross- section area of the stream, 0.15m below the tap would be:$\left ( Take \, \, g=10ms^{-2} \right )$Option 1)$2\times 10^{-5}m^{2}$Option 2)$5\times 10^{-5}m^{2}$Option 3)$5\times 10^{-4}m^{2}$Option 4)$1\times 10^{-5}m^{2}$

using Bernoulli's theorem we get

Velocity at point 2

$V_{2}^{2}-U_{1}^{2}=2gh$

$V_{2}=\sqrt{V_{1}^{2}+2gh}$

$at\, \, \, \, h= 0.15m$

$V_{2}=2m/s$

now use equation of continuity

$A_{1}V_{_{1}}=A_{2}V_{2}$

$\left ( 10^{-4} \right )\left ( 1 \right )=A_{2}\times 2$

$A_{2}=.5\times 10^{-4}$

$A_{2}=5\times 10^{-5}m^{2}$

Option 1)

$2\times 10^{-5}m^{2}$

Option 2)

$5\times 10^{-5}m^{2}$

Option 3)

$5\times 10^{-4}m^{2}$

Option 4)

$1\times 10^{-5}m^{2}$

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