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Question

Two soap bubbles of radii r1 and r2 and pressure P1 and P2 respectively are stuck together with an intermediate film separating them. Choose the correct option(s).

A
The radius of curvature of this film is r1r2|r1r2|
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B
The radius of curvature of this film is r1r2|r1+r2|
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C
If r1>r2 and P2>P1, the intermediate film will bulge towards the center of radius r1
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D
If r1>r2 and P2>P1, the intermediate film will bulge towards the center of radius r2
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Solution

The correct options are
A The radius of curvature of this film is r1r2|r1r2|
C If r1>r2 and P2>P1, the intermediate film will bulge towards the center of radius r1
Excess pressure inside a soap bubble is 4Tr where T is the surface tension.
If P is the atmospheric pressure and if pressure inside soap bubble are P1 and P2, then
P1=4Tr1+P,P2=4Tr2+P
Now, difference of pressure between these two films will decide on which side intermediate film will bulge and radius of curvature of this film.
P1P2=4T|(1r11r2)|=4Tr12
1r12=|1r11r2|
r12=r1r2|r1r2|
As pressure is more on concave side, therefore it will bulge on that side where pressure is less.
Hence, if r1>r2 and P2>P1, the intermediate film will bulge towards the center of radius r1.

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