There is a howizontal film of soap solution. On it a thread is placed in the form of a loop. The film is pierced inside the loop and the thread becomes a circular loop of radius `R`. If the surface tension of the loop be `T`, then what will be the tension in the thread?

Options

A. `(piR^2)/(T)`
B. `piR^2T`
C. `2piRT`
D. `2RT`

Answer

D

Explanation

Suppose tension in thread is `F`, then for small part `trianglel` of thread
`trianglel=Rtheta` and `2Fsin(theta)/(2)=2Ttrianglel=2TRtheta`
`impliesF=(TRtheta)/((sintheta)/(2))=(TRtheta)/((theta)/(2))=2TR((sintheta)/(2)approx(theta)/(2))`