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Question

A tube of fine bore AB is connected to a manometer M as shown. The stopcock S controls the flow of air AB is dipped into a liquid whose surface tension is σ. On opening the stopcock 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 P 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
293389_3aac1830e1fd4bb1915fad08042196be.png

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 D rhρg4
Surface tension of liquid =σ
Difference in pressure =P
Radius of curvature of manometer =r
Equating difference in pressure from Bernoulli's law:
ΔP=4σr=ρgh
σ=ρhrg4

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