question_answer

The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. What is the ratio between the volume of the first and the second bubble?             

Answer:

                Given: \[{{P}_{1}}=3{{P}_{2}}\]                 or                            \[\frac{4\sigma }{{{r}_{1}}}=\frac{3\times 4\sigma }{{{r}_{2}}}\]                 or            \[{{r}_{2}}=3{{r}_{1}}\]                 \[\therefore \]  \[\frac{{{V}_{1}}}{{{V}_{2}}}=\frac{\frac{4}{3}\pi r_{1}^{3}}{\frac{4}{3}\pi r_{2}^{3}}={{\left( \frac{{{r}_{1}}}{{{r}_{2}}} \right)}^{3}}={{\left( \frac{1}{3} \right)}^{3}}=\mathbf{1:27}\]