Two soap bubbles, A and B, have radii in the ratio 3 : 2 . The excess pressure inside the bubble A to that of B is in the ratio

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The excess pressure inside a soap bubble of radius $R$ and surface tension $T$ is given by $Δ P = \frac{4 T}{R}$ .

This implies that the excess pressure is inversely proportional to the radius of the bubble, $Δ P \propto \frac{1}{R}$ .

Given the ratio of radii of bubbles A and B is $R_{A} : R_{B} = 3 : 2$ .

The ratio of their excess pressures is $\frac{Δ P _{A}}{Δ P _{B}} = \frac{R _{B}}{R _{A}} = \frac{2}{3}$ .

Thus, the ratio is $2 : 3$ .

Answer: $2 : 3$

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