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} $
