A film of soap solution is formed on a loop frame loop of `6.28 cm` long thread is gently put on the film and the film is broken with a needle inside the loop. The tread loop takes the shape of a circle. Find the tension in the thread. Surface tension of soap solution `= 0.030 n//m`.

Answer

3

Explanation

When the soap film enclosed by the thread is pricked, the thread would take up a circular shape. Consider a small element of the thread. While horizontal components of tension get balanced, the vertical components get added up. ` sigma ` = surface tension of soap film
or ` 2T sin theta = sigma Delta l since theta ` is very small
So, ` sin theta ~~ theta and Delta l = 2 theta r `
` or 2 T theta = sigma (2 theta xx r ) `
or ` T = sigma r = sigma xx (2 pi r )/(2pi ) = 0.030 xx (6.28 xx 10 ^(-2))/(2pi ) ` N
` = 3 xx 10 ^(-4) N `