The excess pressure inside the first soap bubble of radius R₁ is three times that inside the second soap bubble of radius R₂ . The ratio of volumes of the first to second bubble is

Step-by-step solution

The excess pressure inside a soap bubble of radius R is given by P = 4T R , where T is the surface tension. Given that the excess pressure inside the first bubble is three times that inside the second bubble: P₁ = 3 P₂ 4T R₁ = 3 ( 4T R₂ ) R₁ R₂ = 1 3 The volume of a spherical bubble is V = 4 3 R^3 . The ratio of their volumes is: V₁ V₂ = ( R₁ R₂ )^3 V₁ V₂ = ( 1 3 )^3 = 1 27 The ratio of volumes of the first to the second bubble is 1 : 27 . Answer: 1 : 27