Question

The volume of an air bubble is doubled as it rises from the bottom of lake to its surface. The atmospheric pressure is $75cm$ of mercury. The ratio of density of mercury to that of lake water is $\frac{40}{3}$. The depth of the lake in metre is

• A. 10
• B. 15
• C. 20
• D. 25

Answer 1

Answer: (A)

$2P_0=P_0+\rho gh$
$\Rightarrow P_0=\rho gh$
$\Rightarrow P_0=75cm$ mercury [Atmospheric pressure]

$={\rho }_{\text{mercury }}\times g\times \frac{75}{100}={\rho }_{\text{water }}\times g\times h$
$\Rightarrow \frac{{\rho }_m}{{\rho }_w}\times \frac{75}{100}=h$
$\Rightarrow \frac{40}{3}\times \frac{75}{100}=h=10m$