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

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