When an air bubble of radius r rises from the bottom to the surface of a lake. Its radius becomes 5 r 4 (the pressure of the atmosphere is equal to the 10 ~m height to water column). If the temperature is constant and the surface tension is neglected the depth of the lake is

Step-by-step solution

Initial pressure p₁= atmospheric pressure + pressure of liquid column =h d g+h₁ d gh=10 ~m of water, h₁= depth of lake p₁=d g (h+h₁ ) From, p₁ V₁=p₂ V₂ aligned d g(10+h) 4 3 r₁^3 & =h d g 4 3 r₂^3 (10+h) r^3 & =10 ( 5 4 r )^3 (10+h) & =10 125 64 h & = 1250 64 -10 h & = 610 64 =9.53 ~m aligned