Two soap bubbles of radii R₁ and R₂ are in contact, with R₂ greater than R₁. The common separating soap film is spherical with radius of curvature R(c). Assuming the same surface tension S throughout, which relation is correct?
Options

Question

Two soap bubbles of radii R₁ and R₂ are in contact, with R₂ greater than R₁. The common separating soap film is spherical with radius of curvature R(c). Assuming the same surface tension S throughout, which relation is correct?

Options

G1 Physics · Accepted Answer

The pressures inside the two bubbles are P₁ = P(out)+4S/R₁, P₂ = P(out)+4S/R₂. Therefore, P₁−P₂ = 4S(1/R₁−1/R₂). The common separating film is itself a soap film, so the pressure difference across it is P₁−P₂ = 4S/R(c). Equating, 1/R(c) = 1/R₁−1/R₂. Therefore, R(c) = R₁R₂/(R₂−R₁). Correct option: B.