Question

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

• A.
• B.
• C.
• D.

Answer 1

The correct option is B

If the level in narrow tube goes down by $h_1$ then in wider tube goes up to $h_2$,

$Now,\pi r^2{h}_1=\pi (nr{)}^2{h}_2\Rightarrow h_1=n^2{h}_2$

Now, pressure at point A = pressure at point B

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

$\Rightarrow h=(n^2{h}_2+h_2)sg(Ass=\frac{{\rho }^{\prime }}{\rho })\Rightarrow h_2=\frac{h}{(n^2+1)s}$