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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

$\frac{h}{n^{2} s}$

b

$\frac{n^{2} h}{{(n + 1)}^{2} s}$

c

$\frac{h}{(n^{2} + 1) s}$

d

$\frac{h}{{(n + 1)}^{2} s}$

answer is B.

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Detailed Solution

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$\Rightarrow π r^{2} h_{1} = π (n r)^{2} h_{2} \Rightarrow h_{1} = n^{2} h_{2} N o w p r e s s u r e a t p o i n t A = p r e s s u r e a t p o i n t B h ρ g = (h_{1} + h_{2}) ρ^{'} g \Rightarrow h = (n^{2} h_{2} + h_{2}) sg also s = \frac{ρ^{'}}{ρ} h_{2} = \frac{h}{(n^{2} + 1) s}$

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