When a large bubble rises from bottom of a lake to surface, its radius doubles. If atmospheric press

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9-1.Fluid Mechanics

normal

When a large bubble rises from the bottom of a lake to the surface, its radius doubles. If atmospheric pressure is equal to that of column of water height $H$, then the depth of lake is

$H$

$2H$

$7H$

$8H$

Solution

$\mathrm{P}_{1} \mathrm{V}_{1}=\mathrm{P}_{2} \mathrm{V}_{2}$

$\Rightarrow \quad(\rho \mathrm{g} \mathrm{H}+\rho \mathrm{gh}) \frac{4}{3} \pi \mathrm{R}^{3}=\rho \mathrm{gh} \cdot \frac{4}{3} \pi(2 \mathrm{R})^{3}$

$\Rightarrow \quad \mathrm{H}+\mathrm{h}=8 \mathrm{H}$

$\Rightarrow \quad \mathrm{h}=7 \mathrm{H}$

Standard 11

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When a large bubble rises from the bottom of a lake to the surface, its radius doubles. If atmospheric pressure is equal to that of column of water height $H$, then the depth of lake is

Solution

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