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Q.
Two soap bubbles have radii in the ratio of $2:1$. What is the ratio of excess pressures inside them?
AMUAMU 2008
Solution:
Excess pressure inside the bubble,
$p=\frac{4 T}{r}$
Then, $p_{1}=\frac{4 T}{r_{1}} $ ... (i)
$ P_2 =\frac{4 T}{r_{2}}$ ...(ii)
From Eqs. (i) and (ii), we have
$\frac{p_{1}}{p_{2}}=\frac{4 T / r_{1}}{4 T / r_{2}}=\frac{r_{2}}{r_{1}}$
$\frac{p_{1}}{p_{2}}=\frac{1}{2}$