Question

A wire forming a loop is dipped into soap solution and taken out, so that a film of soap solution is formed. A loop of $6.28em$ long thread is gently put on the film and the film is pricked with a needle inside the loop. The thread loop takes tile shape of a circle. Find the tension in the thread. Surface tension of soap solution $=0.030N/m$

Answer 1

The loop will take circular shape after pricking. Radius of which is given by the relation.
$l=2\pi R$
or $R=\frac{l}{2\pi }$
$=\frac{6.28}{2\times 3.14}$
$=1$ cm
$={10}^{-2}$ m
$2T\sin \left(d\theta \right)$ force in inward direction is balanced by surface tension force in outward direction.
$\therefore$ $2T\sin \left(d\theta \right)=$(Surface tension)$\times$(length of arc)
For small angles, $\sin d\theta =d\theta$
$\therefore$ $2Td\theta =S\left(2Rd\theta \right)$ (S=Surface tension)
T=SR
$=\left(0.030\right)\left({10}^{-2}\right)$
$=3.0\times {10}^{-4}$ N