On heating water, bubbles beings formed at the bottom of the vessel detatch and rise. Take the bubbles to be spheres of radius `R` and amking a circular contact of radius `r` with the bottom of the vessel. If `r ltlt R`, and the surface tension of water is `T`, value of `r` just before bubles detatch is : (density of water is `rho_(w))`

Options

A. `R^(2)sqrt((2rho_(m)g)/(3T))`
B. `R^(2)sqrt((rho_(a)g)/(6T))`
C. `R^(2)sqrt((rho_(ag))/T)`
D. `R^(2)sqrt((3rho_(a)g)/T)`

Answer

A

Explanation

On heating water
`sintheta=r/R`
The bubble will detach if Buoyant force 2 surface tension force
`(rho_(w))(4/3piR^(3))g ge (T)(2pir)sin theta`
Solving `r=sqrt((2rho_(w)R^(4)g)/(3T))`
`sin thea=r/R`