Properties Of Solids And Liquids Question 314

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$ (H+h)\rho g\times \frac{4}{3}\pi r^{3} $

$ =H\times \frac{4}{3}\pi {{(2r)}^{3}} $

$ \Rightarrow H+h=8H $ \ $ h=7H $



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