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On heating water, bubbles being formed a...

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`)

A

(a) `R^2sqrt((rho_wg)/(3T))`

B

(b) `R^2sqrt((rho_wg)/(6T))`

C

(c) `R^2sqrt((rho_wg)/(T))`

D

(d) `R^2sqrt((3rho_wg)/(T))`

Text Solution

Verified by Experts

None of the given option is correct. When the bubble gets detached,
Buoyant force = force due to surface tension

Force due to excess pressure = upthrust
Access pressure in air bubble `=(2T)/(R)`
`(2T)/(R)(pir^2)=(4piR^3)/(3T)rho_wg`
`impliesr^2=(2R^4rho_wg)/(3T)`
`implies r=R^2sqrt((2rho_wg)/(3T))`
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