A flexible closed thread of total length 20π cm is placed on a soap film of surface tension 0.05 N/m. The film inside the thread is punctured and the thread becomes circular. If the tension developed in the thread is N × 10⁻² N, find N.
Physics · Properties of solid and fluid · properties of fluid and surface tension
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Question

A flexible closed thread of total length 20π cm is placed on a soap film of surface tension 0.05 N/m. The film inside the thread is punctured and the thread becomes circular. If the tension developed in the thread is N × 10⁻² N, find N.

Physics · Properties of solid and fluid · properties of fluid and surface tension

G1 Physics · Accepted Answer

The circular thread radius is R = L/(2π). Given, L = 20π cm, so R = 10 cm = 0.10 m. For a soap film, the outward pull per unit length is 2S. Equilibrium of a small arc gives τ = 2SR. Therefore, τ = 2×0.05×0.10 = 0.01 N = 1×10⁻² N. Hence, N = 1.