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Question

Water from a tap emerges vertically downwards with an initial speed of 1 m/s. If the cross-sectional area of tap is 104 m2 then find the cross sectional area of stream 0.15 m below the tap.

A
5×104 m2
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B
1×104 m2
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C
5×105 m2
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D
2×105 m2
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Solution

The correct option is C 5×105 m2
Let us suppose cross-sectional area of stream is Ab and speed of water is vf at 0.15 m below the tap.
Given that,
Initial speed of water (vi)=1 m/s
Cross-sectional area of tap (At)=104 m2

To find the speed of water at 0.15 m below of tap:
Let us consider the mass of water be m
On applying, law of conservation of mechanical energy
M.Ei=M.Ef
12m(vi)2+mgh1=12m(vf)2+mgh2 .........(1)
From the figure, the reference level has been chosen at 0.15 m below the tap, h1=0.15 m and h2=0 m
12×m×12+m×10×0.15=12×m×(vf)2+m×10×(0)

vf=12+2×10×0.15=2 m/s ...(1)
On applying equation of continuity
At vi=Ab vf
104×1=Ab×2 [From (1)] Ab=5×105 m2

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