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Correct Option is B : 20m
Explanation :
Pressure exerted by the liquid at the half of the depth of lake=p1 = P0 +h1dg
pressure at the bottom of the lake= P0+h2dg
where po is atmospheric pressure
According to given condition: pressure at the half of depth of lake is 2/3 pressure at the bottom of lake
P0+h1dg=2/3 (P0+h2dg)
and h1=h2/2
P0+(h2/2)dg=2/3 p0 +2/3 h2dg
on solving we get,1/3Po=1/6 h2dg
h2=2Po/dg
where Po= 1 atm ≈ 10⁵ pascals
d=density of water=1000kg/m³
g≈10m/s²
=2x10⁵/10⁴=20 m
∴ depth of lake is 20m
Explanation :
Pressure exerted by the liquid at the half of the depth of lake=p1 = P0 +h1dg
pressure at the bottom of the lake= P0+h2dg
where po is atmospheric pressure
According to given condition: pressure at the half of depth of lake is 2/3 pressure at the bottom of lake
P0+h1dg=2/3 (P0+h2dg)
and h1=h2/2
P0+(h2/2)dg=2/3 p0 +2/3 h2dg
on solving we get,1/3Po=1/6 h2dg
h2=2Po/dg
where Po= 1 atm ≈ 10⁵ pascals
d=density of water=1000kg/m³
g≈10m/s²
=2x10⁵/10⁴=20 m
∴ depth of lake is 20m
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