Properties of Matter 4 Question 16

18. A soap bubble is being blown at the end of 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 sometime the bubble, having grown to 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.

(2003, 4M)

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Answer:

Correct Answer: 18. 4Tρv2

Solution:

  1. Surface Tension force =2πb×2Tsinθ

Mass of the air per second entering the bubble =ρAv

Momentum of air per second

= Force due to air =ρAv2

The bubble will separate from the tube when force due to moving air becomes equal to the surface tension force inside the bubble.

2πb×2Tsinθ=ρAv2

putting sinθ=br,A=πb2 and solving, we get

r=4Tρv2



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