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

Answer

A

Explanation

The bubble will detach if,
`intsinthetaTxxd,=T(2pir)sintheta`
Buoyant force `ge` surface tension force
`(rho_(w))((4)/(3)piR^(3))ggt(T)(2pir)sintheta`
`impliessintheta=(r)/(R)`