Question

The volume of an air bubble is doubled as it rises from the bottom of lake to its surface. The atmospheric pressure is $75\, cm$ 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)

$2 P_{0}=P_{0}+\rho g h$
$\Rightarrow P_{0}=\rho g h$
$\Rightarrow P_{0}=75\, cm$ mercury [Atmospheric pressure]

$=\rho_{\text {mercury }} \times g \times \frac{75}{100}=\rho_{\text {water }} \times g \times h$
$\Rightarrow \frac{\rho_{m}}{\rho_{w}} \times \frac{75}{100}=h$
$\Rightarrow \frac{40}{3} \times \frac{75}{100}=h=10 m$