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 `rlt ltR` 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((p_(w)g)/(T))`
B. `R^(2) sqrt((3p_(w)g)/(T))`
C. `R^(2) sqrt((p_(w)g)/(3T)`
D. `R^(2) sqrt(p_(w)g)/(6T)`

Explanation

When the bubble gets detached.
Buoyant force =exchange force due to surface tension
`T sin theta (2pir) =4/3 piR^(3) p_(w)g`
`rArr T xx r/R (2pi r)=4/3 piR^(3) p_(w) g`
`rArr r^(2)=(2R^(4)p_(w)g)/(3T)`
`rArr r=R^(2) sqrt((2p_(w)g)/(3T))`