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

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

Mechanical Properties of Fluids

Solution:

According to the relation, $P _{1} V _{1}= P _{2} V _{2}$
$( H + h ) \rho g \times \frac{4}{3} \pi r ^{3}= H \rho g \times \frac{4}{3} \pi(3 r )^{3}$
$( H + h ) r ^{3}=27 Hr ^{3}$
$\Rightarrow h =26 H$