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Question

A tube of fine bore AB is connected to a manometer M as shown. The stop cock S controls the flow of air. AB is dipped into a liquid whose surface tension is σ. On opening the stop cock for a while, a bubble is formed at B and the manometer level is recorded, showing a difference h in the levels in the two arms. If ρ be the density of manometer liquid and r the radius of curvature of the bubble, then the surface tension σ of the liquid is given by

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A
ρhrg
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B
2ρhrg
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C
4ρhrg
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D
rhρg4
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Solution

The correct option is B rhρg4
px=p0+ρgh ......(i)
Now pCp0=4σr
This is the pressure drop in the soap bubble
same air is filled we have px=py=pC
Equating p0 from both the above equations we get
pxρgh=pC4σr.....(ii)
we get σ=ρghr4
139939_71721_ans.png

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