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

Answer

B

Explanation

(b)
If the level in narrow tube goes down be `h_1` then in wider tube goes up to `h_2,`
Now,`pi r^2 h_1 = pi(nr)^2 h_2 rArr h_1 = m^2h_2`
Now, pressure at point A = pressure at point B
`H rho g = (h_1 +h_2) rho'g`
`rArr h = (n^2h_2 + h_2)sg ((As s = (rho')/(rho)) rArr h_2 = (h)/((n^2 + 1)s)`