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 $6.28$cm long thread is gently put on the film and the film is pricked with a needle inside the loop. The thread loop takes the shape of a circle. Find the tension in the thread. Surface tension of soap solution $=0.030N{m}^{-1}$.

Answer 1

$dF=T\times rd\theta$

considering the symmetric elements

${dF}_y=2Trd\theta .sin\theta [{dF}_x=0]$

$F=2Tr{\int }_0^{\pi /2}sin\theta d\theta =2Tr\left[{cos\theta }_0^{\pi /2}\right]=T\times 2r$

tension

$2T_1=T\times 2r⟹T_1=T_r$