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 :
\[\left[ r=\sqrt{\frac{2}{3}\frac{\rho g}{T}}\cdot {{R}^{2}} \right]\] The down ward force on the bubble due to surface tension \[=2\pi r.T\sin \theta \]\[=\frac{2\pi T{{r}^{2}}}{R}\]The upward buoyant force exceeds, the surface tension force then the bubbledetaches. \[\therefore \]\[\frac{4}{3}\pi {{R}^{3}}\rho g=\frac{2\pi T{{r}^{2}}}{R}\]\[\Rightarrow \]\[\left[ r=\sqrt{\frac{2}{3}\frac{\rho g}{T}}\cdot {{R}^{2}} \right]\]You need to login to perform this action.
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