A tube of fine bore `AB` is connected to a manomeer `M` as shown. The stop cock `S` controls the flow in air. `AB` is dipped into a liquid whosw surface tension is `sigma`. On opening the stop cock for a while, a bubble is formed at `B` and the manometer level is recorded, showing a difference `h` in the levels in the two arms. If `rho` be the density of manometer liquid and `r` the radius of curvature of the bubble, then the surface tension `sigma` of the liquid is given by

Options

A. `rhohrg`
B. `2rhohgr`
C. `4rhohrg`
D. `(rhrhog)/(4)`

Answer

D

Explanation

`P_(A)` has to be equal to `P_(B)`.
`P_(A) = P_(0) + rhogh …..(i)`

Now `P_(C) - P_(0) = (4sigma)/(r) :'` soap bubble has `2` films
and `P_(C) = P_(B) :'` same air is filled
`rArr P_(0) + (4sigma)/(r) = P_(0) + rhogh ....(ii)`
get `sigma = (rhogh)/(4)`