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Question

The radii of two columns in a U tube are r1 and r2. When a liquid of density ρ ( angle of contact is 00) is filled in it, the level difference of liquid in two arms is h. The surface tension of liquid is ( g= acceleration due to gravity)

A
ρghr1r22(r2r1)
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B
ρgh(r2r1)2r1r2
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C
2(r2r1)ρghr1r2
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D
ρgh2(r2r2)
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Solution

The correct option is A ρghr1r22(r2r1)
As we know that
Rise of liquid in the capillary tube is given by H=2Trρg

where, T is the surface tension of the liquid, r is the radius of the tube.
Given that h1 is the height in the tube of radius r1 and h2 is the height in tube of radius of r2

h1=2Tr1ρg

h2=2Tr2ρg
Level difference of liquid in the two arms is given by

h=h1h2=2Tr1ρg2Tr2ρg

h=2Tρg[r2r1r1r2]


Hence Surface tension of the liquid, T=hρgr1r22(r2r1)


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