A rectangular film of liquid is expanded from ( 5 ~cm 4 ~cm ) to ( 7 ~cm 8 ~cm ). If the work done is 3 10⁻⁴ ~J , the surface tension of the liquid is (nearly)

Step-by-step solution

The surface tension T is determined from the work done expanding the liquid film, accounting for both surfaces. Initial area is 5 4=20 cm ^2 and final area is 7 8=56 cm ^2 , giving a change per surface of 36 cm ^2 . Since the film has two surfaces, the total area change is 2 36=72 cm ^2 , or 72 10⁻⁴ m ^2 in SI units. The work done is W = T 2 A , so T = W 2 A . Substituting W = 3 10⁻⁴ J and 2 A = 72 10⁻⁴ m ^2 : T = 3 10⁻⁴ 72 10⁻⁴ = 3 72 = 1 24 0.04 N/m . This value corresponds to option B .