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 bubble to second bubble is

Step-by-step solution

The excess pressure inside a soap bubble of radius R is given by P = 4T R . Given that 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 = ( 1 3 )^3 = 1 27 . Thus, the ratio of volumes is 1:27 . Answer: 1:27