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A cylindrical vessel of area of cross-section A is filled with water to a height H. It has capillary tube of length  l and radius r fitted horizontally at its bottom. If the coefficient of viscosity of water is  η, then time required in which level will fall to a height H2 is (density of water is ρ)

a
ηlr24Aρln2
b
4ηlr4πgAρln2
c
8ηlAρπgr4ln2
d
4Hηlρπgr4ln2

detailed solution

Correct option is C

−Adhdt=πhρgr48ηl ⇒∫0tdt=∫HH/2−8ηlAπρgr41hdh   or  t=8ηlAπρgr4ln2

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