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. $
