Question

The excess pressure inside a soap bubble is three times than excess pressure inside a second soap bubble, then the ratio of their surface area is

• A. $ 9 : 1 $
• B. $ 1 : 3 $
• C. $ 1 : 9 $
• D. $ 3 : 1 $

Answer 1

The Correct Option is C

Pressure, $ P=\frac{4S}{r} $ or $ P \propto\frac{1}{r} $ $ \therefore \frac{P_{1}}{P_{2}}=\frac{r_{2}}{r_{1}}=\frac{3}{1} \ldots\left(i\right) $ or $ r_{2}=3r_{1} $ Also $ \frac{A_{1}}{A_{2}}=\frac{4\pi r_{1}^{2}}{4\pi r_{2}^{2}}=\left(\frac{r_{1}}{r_{2}}\right)^{2} =\left(\frac{r_{1}}{3r_{1}}\right)^{2} \left(Using \left(i\right)\right) $ $ =\frac{1}{9} $