There is a horizontal film of soap solution. | vedclass

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(B) Consider a small element of the thread of length $\Delta l$ subtending an angle $	heta$ at the center,where $\Delta l = R	heta$.The soap film ex

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$2RT$

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(B) Consider a small element of the thread of length $\Delta l$ subtending an angle $	heta$ at the center,where $\Delta l = R	heta$.The soap film exerts a force due to surface tension on both sides of the thread. Since the film exists only on the outside,the force per unit length is $T$. For a soap film,there are two surfaces,so the force per unit length is $2T$.The total inward force on the element $\Delta l$ is $F_{net} = (2T) \Delta l = 2TR	heta$.This force is balanced by the radial component of the tension $F$ in the thread: $2F \sin(	heta/2) = 2TR	heta$.For small $	heta$,$\sin(	heta/2) \approx 	heta/2$,so $2F(	heta/2) = 2TR	heta$.$F	heta = 2TR	heta$,which simplifies to $F = 2RT$.

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 soap solution is $T$,what will be the tension in the thread?

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