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 `=0.030Nm^-1`.

Options

A. `1xx10^(4)n`
B. `2xx10^(-4)N`
C. `3xx10^(-4)N`
D. `4xx10^(-4)N`

Answer

C

Explanation

When the soap field enclosed by the thread is pricked, the thread would take up a circular shape. Consider a small element of the thread. While horizontal compnents of tension get balanced, the vertical components get added up.

or `2Tsintheta=sigma/_\l`
or `2Ttheta=sigma(2thetaxxr)`
or `T=sigmar=sigmaxx(2pir)/(2pi)=0.030xx(6.28xx10^(-2))/(2pi)N`
`=3xx10^(-4)N`