Properties Of Solids And Liquids Question 311

Question: Pressure inside two soap bubbles are 1.01 and 1.02 atmospheres. Ratio between their volumes is [MP PMT 1991]

Options:

A) 102 : 101

B)$ {{\left( 102 \right)}^{3}}:{{\left( 101 \right)}^{3}} $

C) 8 : 1

D)2 : 1

Show Answer

Answer:

Correct Answer: C

Solution:

Outside pressure = 1 atm Pressure inside first bubble = 1.01 atm Pressure inside second bubble = 1.02 atm

Excess pressure $ \Delta P _{1}=1.01-1=0.01 $ atm

Excess pressure $ \Delta P _{2}=1.02-1=0.02 $ atm $ \Delta P\propto \frac{1}{r}\Rightarrow r\propto \frac{1}{\Delta P}\Rightarrow \frac{r _{1}}{r _{2}}=\frac{\Delta P _{2}}{\Delta P _{1}}=\frac{0.02}{0.01}=\frac{2}{1} $ Since $ V=\frac{4}{3}\pi r^{3}\ \ \therefore \ \ \frac{V _{1}}{V _{2}}={{\left( \frac{r _{1}}{r _{2}} \right)}^{3}}={{\left( \frac{2}{1} \right)}^{3}}=\frac{8}{1} $



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