The pressure inside two soap bubbles, (A) is 1.01 and that of (B) is 1.02 atmosphere respectively. The ratio of their respective radii (A to B) is (outside pressure = 1 atm .)

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

For bubble A, the excess pressure is $Δ P_{A} = P_{A} - P_{0} = 1.01 - 1 = 0.01 atm$ .

For bubble B, the excess pressure is $Δ P_{B} = P_{B} - P_{0} = 1.02 - 1 = 0.02 atm$ .

Since the radius $R$ is inversely proportional to the excess pressure $Δ P$ , the ratio of their radii is:

$\frac{R _{A}}{R _{B}} = \frac{Δ P _{B}}{Δ P _{A}} = \frac{0.02}{0.01} = \frac{2}{1}$

The ratio of their respective radii is $2 : 1$ .

Answer: $2 : 1$

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