*Problem 1: An air bubble rises from the bottom of a lake to the top and increases its volume 15 times thereby. If the atmospheric pressure is 75 cm and density of lake water is 1.02 **× 10 ^{3 }kg/m^{3}, then find the depth of lake.*

** Solution:** From given information, it is clear that mass and temp. of air inside bubble is constant. Hence applying Boyle’s law,

P_{1}V_{1} = P_{2}V_{2} where 1 represents top & 2 represents bottom.

⇒ P_{1} (15V_{2}) = (P_{1} + ρgh)V_{2}

∴ ρgh = 14 P_{1}

⇒

h = 140 m