A loop of $$6.28$$ cm long thread is put gently on a soap film in a wire loop. The film is pricked with a needle inside the soap film enclosed by the thread. If the surface tension of soap solution is $$0.030$$ $$N/m$$, then the tension in the thread is

Question

Infinity Learn · Accepted Answer

When the soap film enclosed by the thread is pricked, the thread would take up a circular shape. Consider a small element of the thread. While horizontal components of tension get balanced, the vertical components get added $$up.2Tsin$$⁡θ$$=$$σΔ$$l2T$$θ$$=$$σ$$(2$$θ×$$r)T=$$σ$$r=$$σ×$$2$$$$π$$$$r2$$π$$=0.030$$×$$6.28$$×$$10$$−$$22$$π N $$=3$$×$$10$$−$$4$$ N

A loop of 6.28 cm long thread is put gently on a soap film in a wire loop. The film is pricked with a needle inside the soap film enclosed by the thread. If the surface tension of soap solution is 0.030 N/m, then the tension in the thread is

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