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  4. 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 a column of the water height H , then the depth of the lake is (assume temperature remains constant)

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Q. 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 a column of the water height $H$ , then the depth of the lake is (assume temperature remains constant)

NTA AbhyasNTA Abhyas 2020

Solution:

$P_{1} V_{1} = P_{2} V_{2}$
$\Rightarrow $ $\left(\right. H + h \left.\right) \rho g \times \frac{4}{3} \pi r^{3}$ $= H \times \frac{4}{3} \pi \left(\right. 2 r \left.\right)^{3}$
$\Rightarrow H + h = 8 H$
∴ $h = 7 H$