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(A) Consider a small element of the string of length $\Delta l$ subtending an angle $2	heta$ at the center of the circular loop.The force due to surf

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$Td$

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(A) Consider a small element of the string of length $\Delta l$ subtending an angle $2	heta$ at the center of the circular loop.The force due to surface tension $S$ acting on the string is $F_s = 2 	imes S 	imes \Delta l$,where the factor of $2$ accounts for the two surfaces of the soap film.For a small angle $2	heta$,the length $\Delta l = r(2	heta)$,where $r$ is the radius of the loop.The radial component of the tension $T_{str}$ in the string provides the necessary centripetal force to balance the surface tension force.$2 T_{str} \sin 	heta = 2 S \Delta l$Since $	heta$ is very small,$\sin 	heta \approx 	heta$ and $\Delta l = 2r	heta$.$2 T_{str} 	heta = 2 S (2r	heta)$$T_{str} = 2Sr$Since $d = 2r$,we have $T_{str} = S d$.Given the surface tension is $T$,the tension in the string is $T_{str} = Td$.

$A$ massless inextensible string in the form of a loop is placed on a horizontal film of soap solution of surface tension $T$. If the film is pierced inside the loop and it converts into a circular loop of diameter $d$,then the tension produced in the string is ..........

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