A closed flexible thread of length L is placed on a plane soap film. The film inside the thread is punctured while the film outside remains intact. The thread becomes circular. If the surface tension of the soap solution is S, what tension develops in the thread?
Options

Question

A closed flexible thread of length L is placed on a plane soap film. The film inside the thread is punctured while the film outside remains intact. The thread becomes circular. If the surface tension of the soap solution is S, what tension develops in the thread?

Options

G1 Physics · Accepted Answer

When the inside film is punctured, the outside soap film pulls the thread outward. A soap film has two surfaces, so the pull per unit length on the thread is 2S. If the circular thread has radius R, L = 2πR, so R = L/(2π). Consider a small arc subtending dθ. Resultant inward force due to thread tension: τ dθ. Outward surface-tension force on the arc of length R dθ: 2S(R dθ). Equilibrium gives τ dθ = 2SR dθ. Therefore, τ = 2SR = 2S[L/(2π)] = SL/π. Correct option: B.