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

Answer 1

Answer: (A)

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