Two soap bubbles of radius 2 cm and 4 cm, respectively, are in contact with each other. The radius of curvature of the common surface, in cm, is __________. [2025]

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Solution

Q.
Two soap bubbles of radius 2 cm and 4 cm, respectively, are in contact with each other. The radius of curvature of the common surface, in cm, is __________. [2025]

Ans.
(4)

The excess pressure inside a soap bubble is given by the formula,

$△ P = \frac{4 T}{R}$ , where

T is the surface tension of the soap solution, and R is the radius of the bubble.

For the first bubble ( $R_{1}$ = 2 cm) : $△ P_{1} = \frac{4 T}{R_{1}}$

For the first bubble ( $R_{2}$ = 4 cm) : $△ P_{2} = \frac{4 T}{R_{2}}$

When the two bubbles join, the difference in pressure between the two bubbles will equal the pressure difference across the interface (R):

$△ P_{1} - △ P_{2} = △ P$

$\Rightarrow \frac{4 T}{R_{1}} - \frac{4 T}{R_{2}} = \frac{4 T}{R}$

$\Rightarrow R = \frac{R_{1} \cdot R_{2}}{R_{2} - R_{1}} = \frac{2 \cdot 4}{4 - 2} = 4 cm$

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