The pressures inside two soap bubbles A and B are 1.02 atmosphere and 1.04 atmosphere respectively. The ratio of volume of bubble A to that of bubble B is (outside pressure = 1 atmosphere)

Step-by-step solution

The excess pressure inside a soap bubble is given by P = 4T R , where T is the surface tension and R is the radius of the bubble. For bubble A, the excess pressure is P_A = 1.02 - 1 = 0.02 atm. For bubble B, the excess pressure is P_B = 1.04 - 1 = 0.04 atm. Taking the ratio of the excess pressures, we get P_A P_B = 0.02 0.04 = 1 2 . Since R 1 P , the ratio of their radii is R_A R_B = P_B P_A = 2 1 . The volume of a spherical bubble is V = 4 3 R^3 , which means V R^3 . The ratio of their volumes is V_A V_B = ( R_A R