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Question

The radii of the two columns in U-tube are r1 and r2. When a liquid of density ρ (angle of contact is 0) is filled in it, the level difference of liquid in two arms is Δh. The surface tension of liquid is
(g= acceleration due to gravity and r1<r2)

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(r2r1)
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Solution

The correct option is A ρghr1r22(r2r1)

We know,
h=2Tcosθrρg
For limb 1,
h1=2Tcos0r1ρg=2Tr1ρg
Similarly,
For limb 2,
h2=2Tcos0r2ρg=2Tr2ρg
Given,
h1h2=Δh
2Tr1ρg2Tr2ρg=Δh
2Tρg(1r11r2)=Δh
2Tρg(r2r1r1r2)=Δh
T=Δhρgr1r22(r2r1)

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