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(r2−r1)As we know thatRise of liquid in the capillary tube is given by H=2Trρgwhere, 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=2Tr2ρgLevel difference of liquid in the two arms is given byh=h1−h2=2Tr1ρg−2Tr2ρg⟹h=2Tρg[r2−r1r1r2]Hence Surface tension of the liquid, T=hρgr1r22(r2−r1)

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