Question

Pressure inside two soap bubbles are 1.01 atm and 1.03 atm. Ratio between their volumes is

• A. $ 27:1 $
• B. $ 3:1 $
• C. $ 127:101 $
• D. None of these

Answer 1

The Correct Option is A

Excess pressure as compared to atmosphere inside bubble A is $ \Delta {{p}_{1}}=1.01-1=0.01\text{ }atm $ inside bubble B is $ \Delta {{p}_{2}}=1.03-1=0.03\text{ }atm $ Also when radius of a bubble is r, formed from a solution whose surface tension is t, then excess pressure inside the bubble is given by $ p=\frac{4t}{r} $ Let $ {{r}_{1}} $ be the radii of bubbles A and B respectively then $ \frac{{{p}_{1}}}{{{p}_{2}}}=\frac{4T/{{r}_{1}}}{4T/{{r}_{2}}}=\frac{0.01}{0.03} $ $ \frac{{{r}_{2}}}{{{r}_{1}}}=\frac{1}{3} $ Since bubbles are spherical in shape their volumes are in the ratio $ \frac{{{V}_{1}}}{{{V}_{2}}}=\frac{\frac{4}{2}\pi r_{1}^{3}}{\frac{4}{3}\pi r_{2}^{3}} $ $ {{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{3}}={{\left( \frac{3}{1} \right)}^{3}}=\frac{27}{1} $ $ {{V}_{1}}:{{V}_{2}}=27:1 $