Two communicating vessels contain mercury. The diameter of one vessel in n times larger then 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

Options

A. `(n^2 h)/((n+1)^2 s)`
B. `(h)/((n^2+1)s)`
C. `(h)/((n+1)^2 s)`
D. `(h)/(n^2 s)`

Answer

B

Explanation

Volume is same -
`pi r^2 xx h_1=pi(n r)^2 h_2 implies h_2=(h_1)/(n^2)=(h)/(n^2)`
Pressure at interface-
`h rho g=(H_1+H_2)xx rho. g`
`implies h=(n^2 h_2+h_2)(rho.)/(rho) implies h_2=(h)/((n^2+1)s)` `["As s = " (rho.)/(rho)]`