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  4. The excess pressure inside a soap bubble A is twice that in another soap bubble B. The ratio of volumes of A and B is

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Q. The excess pressure inside a soap bubble A is twice that in another soap bubble B. The ratio of volumes of A and B is

Rajasthan PMTRajasthan PMT 2011

Solution:

Excess pressure inside the bubble is $ p=\frac{4T}{r} $ Here, $ {{p}_{A}}=2{{p}_{B}} $ $ \frac{{{p}_{A}}}{{{p}_{B}}}=\frac{{{r}_{B}}}{{{r}_{A}}} $ So, radius of bubble $ B $ is $ {{r}_{B}}=2 $ Ratio of volumes $ \frac{{{V}_{A}}}{{{V}_{B}}}={{\left( \frac{{{r}_{A}}}{{{r}_{B}}} \right)}^{3}}={{\left( \frac{1}{2} \right)}^{3}} $ $ \frac{{{V}_{A}}}{{{V}_{B}}}=\frac{1}{8} $