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Q.

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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a

3×104N

b

4×104N

c

2×104N

d

1×104N

answer is C.

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Detailed Solution

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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.

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 or 2Tsinθ=σΔl or  2Tθ=σ(2θ×r) or  T=σr=σ×2πr2π=0.030×6.28×1022πN                                          =3×104N

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