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

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

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

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

answer is B.

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Detailed Solution

If the level in narrow tube goes down by $h_{1}$ then in wider tube goes up to $h_{2}$ ,

Now, ${πr}^{2} h_{1} = π {(nr)}^{2} h_{2} \Rightarrow h_{1} = n^{2} h_{2}$

Now, pressure at point A = pressure at point B

$hρg = (h_{1} + h_{2}) ρ^{'} g$

$\Rightarrow h = (n^{2} h_{2} + h_{2}) sg (As s = \frac{ρ^{'}}{ρ})$

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

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