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Question

If pressure at half depth of a lake is equal to 23rd pressure at the bottom of the lake, then what is the depth of the lake?
(Take atmospheric pressure as 105 Pa, density of water as 1000 kg/m3 and g=10 m/s2)

A
6.67 m
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B
60 m
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C
10 m
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D
20 m
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Solution

The correct option is D 20 m
Let h be the depth of lake and Po be the atmospheric pressure.
According to the question,
Pressure at half depth of lake
=23× (Pressure at bottom of lake)
Po+ρgh2=23(ρgh+Po)
3(Po+ρgh2)=2(ρgh+Po)
[Po=105 Pa,ρ=103 kg/m3]
3Po+32ρgh=2ρgh+2Po
Po=(232)ρgh
Po=ρgh2
h=2Poρg=2×105103×10=20 m

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