A soap film is formed on a circular frame. A | vedclass

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(C) When the film inside the thread loop is broken,the surface tension of the remaining film outside the loop pulls the thread outwards in all directi

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$RT$

Vedclass · Answer

(C) When the film inside the thread loop is broken,the surface tension of the remaining film outside the loop pulls the thread outwards in all directions,making it circular.Consider a small element of the thread of length $\delta \ell$. The surface tension $T$ acts on this element radially outwards. The force due to surface tension is $F = T \cdot \delta \ell$.Let $T'$ be the tension in the thread. The force balance on the small element $\delta \ell$ in the radial direction is:$2 T' \sin 	heta = T \delta \ell$Since $	heta$ is very small,$\sin 	heta \approx 	heta$. Also,the arc length $\delta \ell = R(2	heta)$.Substituting these into the equation:$2 T' 	heta = T(2 	heta R)$$T' = RT$Thus,the tension in the thread is $RT$.

$A$ soap film is formed on a circular frame. $A$ loop of thread is lying on the film. If the film inside the loop is broken,then the tension in the thread will be: ($R =$ radius of the loop,$T =$ surface tension of the liquid)

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