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(r2−r1)
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B
ρgh(r2−r1)2r1r2
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C
2(r2−r1)ρghr1r2
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D
ρgh2(r2−r1)
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Solution
The correct option is Aρghr1r22(r2−r1)
We know, h=2Tcosθrρg
For limb 1, h1=2Tcos0∘r1ρg=2Tr1ρg
Similarly,
For limb 2, h2=2Tcos0∘r2ρg=2Tr2ρg
Given, h1−h2=Δh ∴2Tr1ρg−2Tr2ρg=Δh ⇒2Tρg(1r1−1r2)=Δh ⇒2Tρg(r2−r1r1r2)=Δh ⇒T=Δhρgr1r22(r2−r1)