The excess pressure inside first soap bubble is three times that of a second soap bubble. The ratio of volumes of the first to second bubble

Step-by-step solution

Given that the excess pressure P₁ in the first soap bubble is three times that in the second, P₂ , we have P₁ = 3P₂ . Using the formula for excess pressure in a soap bubble, P = 4T R , we substitute to obtain 4T R₁ = 3 ( 4T R₂ ) . Cancelling the common factor 4T yields 1 R₁ = 3 R₂ , which simplifies to R₂ = 3R₁ . The volume of a sphere is V = 4 3 R^3 , so the volume ratio is V₁ V₂ = R₁^3 R₂^3 = ( R₁ R₂ )^3 . Substituting R₁ R₂ = 1 3 gives V₁ V₂ = ( 1 3 )^3 = 1 27 . Final Answer: C