| On heating water, bubbles being formed at the bottom of the vessel detatch 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 detatch is : (density of water is \[{{\rho }_{w}}\]) [JEE MAIN 2014] |
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A) \[{{R}^{2}}\sqrt{\frac{{{\rho }_{w}}g}{T}}\]
B) \[{{R}^{2}}\sqrt{\frac{3{{\rho }_{w}}g}{T}}\]
C) \[{{R}^{2}}\sqrt{\frac{{{\rho }_{w}}g}{3T}}\]
D) \[{{R}^{2}}\sqrt{\frac{{{\rho }_{w}}g}{6T}}\]
Correct Answer: D
Solution :
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[d] The down ward force on the bubble due to surface tension   |
| The upward buoyant force exceeds, the surface tension force then the bubble detaches. |
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