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

Options

A. `R^(2)sqrt((rho_(w)g)/(3T))`
B. `R^(2)sqrt((2rho_(w)g)/(3T))`
C. `R^(2)sqrt((rho_(w)g)/(T))`
D. `R^(2)sqrt((3rho_(W)g)/(3T))`

Answer

B

Explanation

`sintheta = (r)/(R)`
The bubble will detach if -
Buoyant force `ge` Surface tension force
`(rho_(w))((4)/(3)piR^(3))g ge (T)(2pir)sin theta`
Solving `r = sqrt((2rho_(w)R^(4)g)/(3T))`
No option matches with the correct Answer (BONUS).
`sintheta = (r)/(R)`