Two soap bubbles of radii 4 cm and 5 cm are touching each other over a common surface $S_{1} S_{2}$ (shown in figure), its radius will be

4 cm

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20 cm

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5 cm

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4.5 cm

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Solution

The correct option is B 20 cm
If radius of curvature of common surface $S_{1} S_{2}$ is $R$ and $R_{1}$ and $R_{2}$ are the radii of touching soap bubbles, then relation between them can be calculated from,
$\frac{4 T}{R} = \frac{4 T}{R_{1}} - \frac{4 T}{R_{2}}$
$∴ \frac{1}{R} = \frac{1}{R_{1}} - \frac{1}{R_{2}}$
$R = \frac{R_{1} R_{2}}{| R_{2} - R_{1} |}$
$R = \frac{5 \times 4}{5 - 4} = 20 c m$

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