There is a horizontal film of soap solution. On it a thread is pl… - Vidyadip

MCQ

There is a horizontal film of soap solution. On it a thread is placed in the form of a loop. The film is pierced inside the loop and the thread becomes a circular loop of radius $R$. If the surface tension of the loop be T, then what will be the tension in the thread

A
$\pi {R^2}/T$
B
$\pi {R^2}T$
C
$2\pi RT$
✓
$2RT$

✓

Answer

Correct option: D.

$2RT$

d
(d) Suppose tension in thread is F, then for small part $\Delta l$ of thread

$\Delta l = R\theta $ and $2F\sin \theta /2 = 2T\Delta l = 2TR\theta $

$ \Rightarrow F = \frac{{TR\theta }}{{\sin \theta /2}} = \frac{{TR\theta }}{{\theta /2}} = 2TR(\sin \theta /2 \approx \theta /2)$

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