Question

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

• A. $Td$
• B. $\pi Td$
• C. $\pi d^{2}T$
• D. $\frac{\pi d^{2}T}{4}$

Answer 1

The correct option is A $Td$

T(surface tension)

d-diameter of loop

At equillibrium

$2T\Delta l=2F\sin \frac{\theta }{2}$

since $\theta$ is very small so $\sin \frac{\theta }{2}\approx \frac{\theta }{2}$

$T\Delta l=F\theta /2$

$\Delta l=r\theta =\frac{d\theta }{2}$

so, $T\times \frac{d\theta }{2}=F\times \frac{\theta }{2}$

$F=Td$.