Q. The volume of an air bubble becomes three times as it rises from the bottom of a lake to its surface. Assuming atmospheric pressure to be $75\ cm$ of $Hg$ and the density of water to be 1/10 of the density of mercury, the depth of the lake is
A) $5\ m$
B) $10\ m$
C) $15\ m$
D) $20\ m$
Explanation
(c) $P_{1}V_{1} = P_{2}V_{2} \Rightarrow \left( P_{0} + h\rho g \right)V = P_{0} \times 3V$
$\Rightarrow h\rho g = 2P_{0} \Rightarrow h = \frac{2 \times 75 \times 13.6 \times g}{\frac{13.6}{10} \times g} = 15\ m$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.