Two separate air bubbles (radii `0.002 cm` and `0.004`) formed of the same liquid (surface tension `0.07 N//m`) come together to form a double bubble. Find the radius and the sense of curvature of the internal film surface common to both the bubbles.

Explanation

Let `R_A and R_B` be the radii of cuvarture of two air bubbles A and B. Let R be the radius of curvature of common surface when two bubbles a and B come together,

The excases presure in bubbles A, `P_A = 4 S//R_A` and the excess pressrue in bubble B, `P_B = 4 S//R_B` As R is the radius of curvature of the common interface, therefore, `P_A - P_B = 4 S//R.`
or `(4S)/(R_A) - (S)/(R_B) = (4S)/(R ) or (1)/(R_A) - (1)/(R_B) = (1)/(R )`
or `R = (R_A R_B)/(R_B -R_A) = (0.002 xx 0.004)/(0.004 - 0.002) = 0.004 m` We know that the excess pressure is more towards concave surface and is inversely proportional to radius of the bubble, therefore the concave surface bubble as shown by dotted. curve.