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

Answer: (A)

By force balancing in vertical direction
$S_F=2T\sin \theta$
$S_F=2T\theta$
$S\times 2r\times 2\theta =2\times T\times \theta$
$\{\because \theta \text{ is small }\sin \theta \simeq \theta$
$S\times 2r=$ Tension
$S\times d=$ Tension
$\{r-\text{radius }d-\text{diameter }$
$\because S=T$
So, Tension $=Td$
Where,
$S_F=$ Force due to surface tension
$T=$ Tension in string
$\theta =$ Small angle
$S=$ Surface tension