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

Answer

B

Explanation

If the level in the narrow tube goes down by `y_1` then in wider tube goes up to `y_2`.
`pi r^2 y_1 = pi (nr)^2 y_2 rArr y_1 = n^2 y_2`
`p_A = p_B`
`rho gh = rho_m g(y_1 + y_2)`
`rho gh = s rho g(n^2 y_2 + y_2)`
`y_2 = (h)/(s(n^2 + 1))`.