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Q.

When a capillary tube of radius r is immersed in a liquid of density ρ, the liquid rises to a height h in it. If m is the mass of the liquid in the capillary tube, the potential energy of this mass of the liquid in the tube is

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a

m g h / 2

b

m g h

c

m g h / 4

d

2 m g h

answer is B.

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Detailed Solution

The mass of the liquid in a column between x and x+d x is
dm=πr2ρdx
Therefore, the potential energy of the liquid in a column of height h is
∫0hπr2xρgdx=πr2ρg∫0hxdx =πr2ρgh22=πr2hρgh/2 =mgh/2

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