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A soap film of surface tension T is formed on a rectangular wire frame. A closed thread loop of length L is placed on the film in an irregular shape. A hole is pierced inside the loop with a needle (so the film inside the loop is destroyed). The thread settles into its equilibrium shape. Select the correct option(s).

1. The thread will take a square shape.
2. The thread will take a circular shape.
3. The tension in the thread will be 2T.
4. The tension in the thread will be T*L / (2*pi)

Correct answer: The thread will take a circular shape.

Solution

When the film inside the loop is pricked, the film outside the loop pulls the thread outward. Since the film exerts the same force per unit length (2T) all around, the thread assumes a circular shape to be in equilibrium. By the relation for a curved thread under uniform outward pressure: 2T = T_thread/r, and circumference L = 2*pi*r, so T_thread = 2T*r = 2T*L/(2*pi) = T*L/pi. The tension in the thread is T*L/pi.

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