Question

Two communicating cylindrical vessel 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 vessel.The mercury level will rise in the right - hand vessel (s=relative density of mercury and p = density of water ) by

• A. $\frac{n^h}{(n+1{)}^{2}s}$
• B. $\frac{h}{(n^2+1)s}$
• C. $\frac{h}{(n+1{)}^{2}s}$
• D. $\frac{h}{\left(n^{2}s\right)}$

Answer 1

The correct option is B $\frac{h}{(n^2+1)s}$

It is given that the diameter of one vessel is n times larger than the diameter of other. So,

$\pi r^2{h}_1=\pi {\left(nr\right)}^2{h}_2$

$h_1=n^2{h}_2$

Since, pressure at point A is equal to pressure at B

$\rho gh=(h_1+h_2){\rho }^{\prime }g$

$\because s=\frac{{\rho }^{\prime }}{\rho }$

$\rho gh=(n^2{h}_2+h_2)s\rho g$

$h_2=\frac{h}{(n^2+1)s}$