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The volume of an air bubble is double as is rises from the button of the lake to the surface.if the atmosphere pressure is H metre of Hg and the density of Hg is n times that of lake water.find the depth of the lake

The volume of an air bubble is double as is rises from the button of the lake to the surface.if the atmosphere pressure is H metre of Hg and the density of Hg is n times that of lake water.find the depth of the lake

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Grade:11

1 Answers

Rituraj Tiwari
askIITians Faculty 1792 Points
3 years ago
ratio of the volume of the air bubble at the top to the bottom, V'/V = 2,

=> V' = 2V

ratio of the density of the mercury to that of the lake water, ρ'/ρ = 40/3

=>ρ' = (40/3) ρ

Now, the pressure exerted at the surface is equal to 75 cm of mercury, so here depth = 0.75 m

the pressure exerted at the bottom will be P at depth = pressure due to water column h + atmospheric pressure, here, h is the depth of the lake

so, the equation would be P' V' = P V

where P = hρg + atmospheric pressure

h is equal to 10 m

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