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 $\rho = $ density of water) by
Diffcult
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(b)If the level in narrow tube goes down by $h_1$ then in wider tube goes up to $h_2,$
Now, $\pi {r^2}{h_1} = \pi {(nr)^2}{h_2}$==> ${h_1} = {n^2}{h_2}$
Now, pressure at point A = pressure at point B
$h\rho g = ({h_1} + {h_2})\rho 'g$
==> $h =$ $({n^2}{h_2} + {h_2})sg$ $\left( {{\rm{As}}\;s = \frac{{\rho '}}{\rho }} \right)$ ==> ${h_2} = \frac{h}{{({n^2} + 1)s}}$
Now, $\pi {r^2}{h_1} = \pi {(nr)^2}{h_2}$==> ${h_1} = {n^2}{h_2}$
Now, pressure at point A = pressure at point B
$h\rho g = ({h_1} + {h_2})\rho 'g$
==> $h =$ $({n^2}{h_2} + {h_2})sg$ $\left( {{\rm{As}}\;s = \frac{{\rho '}}{\rho }} \right)$ ==> ${h_2} = \frac{h}{{({n^2} + 1)s}}$
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