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  • 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

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 r << R, and the surface tension of water is T, value of r just before bubbles detach is :(density of water is \rho _w )

Option: 1

R^{2}\sqrt{\frac{2p_{w}g}{3T}}


Option: 2

R^{2}\sqrt{\frac{p_{w}g}{6T}}


Option: 3

R^{2}\sqrt{\frac{p_{w}g}{T}}


Option: 4

R^{2}\sqrt{\frac{3p_{w}g}{T}}


Answers (1)

best_answer

Here T is the surface tension and we know that surface tension,

 T=\frac{F}{l}=F=Tl=T(2\pi r),

where F is the force due to surface tension and its vertical component will be T(2\pi r)Sin\theta.

Now The bubble will detach, if Buoyant force ≥ vertical component of surface tension force, so for the bubble to just detach:-

vertical component of surface tension force=buoyant force(or upthrust)

T(2\pi r)Sin\theta=V\rho_wg\\\Rightarrow T(2\pi r)\frac{r}{R}=\frac{4}{3}\pi R^3\rho_wg\\ \Rightarrow r^2=\frac{2R^4\rho_wg}{3T}\\ \Rightarrow r=R^2\sqrt{\frac{2\rho_wg}{3T}}

Posted by

sudhir.kumar

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