Properties Of Solids And Liquids Question 289

Question: When a large bubble rises from the bottom of a lake to the surface. Its radius doubles. If atmospheric pressure is equal to that of column of water height H, then the depth of lake is [AIIMS 1995; AFMC 1997]

Options:

A)H

B)2H

C)7H

D)8H

Show Answer

Answer:

Correct Answer: C

Solution:

$ P _{1}V _{1}=P _{2}V _{2} $

therefore $ (P _{0}+h+g)\times \frac{4}{3}\pi r^{3} $ =$ P _{0}\times \frac{4}{3}\pi {{(2r)}^{3}} $

Where, h = depth of lake

therefore $ h\rho g=7P _{0} $

therefore $ h=7\times \frac{H\rho g}{\rho g}=7H. $



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