A soap bubble is being blown at the end of a very narrow tube of radius b. Air (density ρ) moves with a velocity ‘v’ inside the tube and comes to rest inside the bubble. The surface tension of the soap solution is T. After some time the bubble, having grown to a radius ‘r’, separates from the tube. Find the value of ‘r’. Assume that r>>b so that you can consider the air to be falling normally on the bubble’s surface.

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$\frac{4 T}{ρv}$

$\frac{4 T}{{ρv}^{2}}$

$\frac{2 T}{{ρv}^{2}}$

$\frac{4 T}{{ρv}^{3}}$

answer is D.

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Detailed Solution

The bubble will separate from the tube when thrust force exerted by the air is equal to the force due to excess pressure.
$i.e. {ρAv}^{2} = (\frac{4 T}{r}) A or r = \frac{4 T}{{ρv}^{2}}$

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