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`.

Answer

A, C, D

Explanation

The loop will take circular shape after pricking. Raduis of which is given by the relation.

`l=2(pi)R` or `R=(1)/(2 pi)=(6.28)/(2xx3.14)=1 cm`
`=10^(-2) m`
`2T sin d theta` force in inward direction is balanced by surface tension force in out ward dirction.
`:. 2T sin (theta)=("surface tension")xx("length of are" )`
For small angles. `sin d(theta)=d(theta)`
`:. 2Td(theta)=S(2Rd theta) (S=`Surface tension)
`:. T=SR`
`=(0.020)(10^(-2))`
`=3.0xx10^(-4)N`.