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

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  1. 4S/R
  2. 35/R
  3. 6S/R
  4. None of these

Answer (Detailed Solution Below)

Option 3 : 6S/R
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Concept: Excess pressure inside a soap bubble is given by 4S / R due to two surfaces (inner and outer) under surface tension.

Let:

P0 = Atmospheric pressure

P1 = Pressure inside the larger bubble (radius 2R)

P2 = Pressure inside the smaller bubble (radius R)

Pressure inside the larger bubble:

P1 = P0 + 4S / (2R) = P0 + 2S / R

Pressure difference between smaller and larger bubble:

P2 - P1 = 4S / R

Substituting from (i) and (ii):

P2 - P0 = (P2 - P1) + (P1 - P0)

= (4S / R) + (2S / R) = 6S / R

Answer: Option 3) 6S / R

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