Question

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

• A. H
• B. 2H
• C. 7H
• D. 8H

Answer 1

The correct option is C 7H

$P_1{V}_1=P_2{V}_2\Rightarrow (P_0+h\rho g)\times \frac{4}{3}{\pi }^3=P_0\times \frac{4}{3}\pi (2r{)}^3$
Where, h = depth of lake
$\Rightarrow h\rho g=7P_0\Rightarrow h=7\times \frac{H\rho g}{\rho g}=7H$