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Q.

Two communicating vessels contain mercury. The diameter of one vessel is n times larger than the diameter of the other. A column of water of height h is poured into the left vessel. The mercury level will rise in the right hand vessel (s = relative density of mercury and ρ = density of water) by

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a

n2h(n+1)2s

b

h(n2+1)s

c

h(n+1)2s

d

hn2s

answer is B.

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Detailed Solution

If the level in narrow tube goes down by h1 then in wider tube goes up to h2,Now, πr2h1 = π(nr)2h2 ⇒h1 = n2h2Now, pressure at point A = pressure at point Bhρg = (h1+h2)ρ'g⇒h = (n2h2+h2)sg (As s = ρ'ρ) ⇒h2 = h(n2+1)s

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