First slide

Surface tension

Question

Two soap bubbles of radii r₁and $r_{2}, (r_{1} > r_{2})$ get attached to each other to have a common interface. The radius of this interface is

Moderate

A

$r_{1} + r_{2}$
B

$r_{1} - r_{2}$
C

$r_{1} r_{2} / (r_{1} + r_{2})$
D

$r_{1} r_{2} / (r_{1} - r_{2})$

Solution

. Let r be the radius of common interface. Then
$P_{1} - P = \frac{4 T}{r_{1}} and P_{2} - P = \frac{4 T}{r_{2}} ∴ P_{2} - P_{1} = 4 T [\frac{1}{r_{2}} - \frac{1}{r_{1}}] Further P_{2} - P_{1} = \frac{4 T}{r} From eqs . (1) and (2), we get \frac{4 T}{r} = 4 T [\frac{1}{r_{2}} - \frac{1}{r_{1}}] = 4 π [\frac{r_{1} - r_{2}}{r_{1} I_{2}}] r = (\frac{r_{1} r_{2}}{r_{1} - r_{2}})$

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