A soap bubble A of radius 0 . 03 m and another bubble B of radius 0 . 04 m coalesce to form a combined bubble such that the radius of curvature of their common interface is r . Then, the value of r is

Step-by-step solution

Let the radius of curvature of the common internal film surface of the double bubble formed by two bubbles A and B be r . Excess of pressure as compared to the atmosphere inside A is p 1 = 4 T r 1 = 4 T 0 .03 Excess of pressure inside B is p 2 = 4 T r 2 = 4 T 0 .04 In the double bubble, the pressure difference between A and B on either side of the common surface is 4 T 0 .03 - 4 T 0 .04 = 4 T r ⟹   1 0 .03 - 1 0 .04 = 1 r ⟹   r = 0 .03 × 0 .04 0 .01 = 0 .12   m