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

Answer

C

Explanation

when bubble gets detached,

buoyant force = force due to surface tension
`(4)/(3)pi R^(3) rho_(w)g =(2pi r)T sin theta =2pi rxxTxx(r)/(R)`
or `r^(2)=(2R^(4)rho_(w)g)/(3T)` or `r=R^(2)sqrt((2rho_(w)g)/(3T))`