question_answer

Equal volumes of two immiscible liquids of densities \[\rho \] and \[2\rho \] are filled in a vessel as shown in figure. Two small holes are punched at depth \[h/2\]and \[3h/2\] from the surface of lighter liquid. If\[{{v}_{1}}\] and \[{{v}_{2}}\] are the velocities of a flux at these two holes, then \[{{v}_{1}}/{{v}_{2}}\]is

A) \[\frac{1}{2\sqrt{2}}\]

B) \[\frac{1}{2}\]  

C) \[\frac{1}{4}\]

D) \[\frac{1}{\sqrt{2}}\]

Correct Answer: D

Solution :

[d] \[{{v}_{1}}=\sqrt{2}g(h/2).\]             For \[{{v}_{2}}\] we can replace the liquid of density\[\rho \] and   height h to a liquid of density \[2\rho \] and height\[h/2\]  Thus \[{{v}_{2}}=\sqrt{2gh}=\sqrt{2v}\].