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A soap bubble of radius R is surrounded by another soap bubble of radius 2R as shown. Taking surface tension = S, the pressure inside the smaller soap bubble, in excess of the atmospheric pressure will be

A
4S4
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B
3S4
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C
6S4
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D
None of these
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Solution

The correct option is C 6S4
Let the pressure inside smaller soap bubble be P2, bigger soap bubble be P1 and atmospheric pressure be Po

Excess pressure across bigger soap bubble and atmosphere,
P1Po=4S2R=2SR(1)
where S is the surface tension.
Excess pressure across bigger bubble and smaller bubble,
P2P1=4SR(2)
Adding (1) and (2)
P2Po=6SR
Hence pressure inside smaller soap bubble in excess of atmospheric pressure is 6SR

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