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When the lower end of a vertical capillary tube of radius r is dipped in water, water rises in it due to capillarity action and change in gravitational potential energy of water is U. If the tube is replaced by another tube of radius 2r, charge in gravitational potential energy will be

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a

4U

b

2U

c

U/2

d

U

answer is D.

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Detailed Solution

Capillary rise, h=2TρrgMass of water in the tube, m=πr2hρ∴ Charge in gravitational potential energy U=mgh2=12(πr2hρ).g.h=π2r2ρg.(2Tρrg)2=2πT2ρgSo change in gravitational potential energy is independent of r∴ U1=U

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When the lower end of a vertical capillary tube of radius r is dipped in water, water rises in it due to capillarity action and change in gravitational potential energy of water is U. If the tube is replaced by another tube of radius 2r, charge in gravitational potential energy will be