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On heating water, bubbles beings formed ...

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

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))`

Text Solution

Verified by Experts

The correct Answer is:
B
`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)`
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