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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a
4Tρv3
b
4Tρv
c
2Tρv2
d
4Tρv2
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. ρAv2=4TrA or r=4Tρv2