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Two large tanks A and B, open at the top, contain different liquids. A small hole is made in the side of each tank at the same depth h below the liquid surface, but the hole in A has twice the area of the hole in B. The ratio of the densities of the liquids in A and B such that the mass flux is the same for each hole should be

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Detailed Solution

Mass flux $= v_{A} A_{A} ρ_{A} = v_{B} A_{B} ρ_{B}$

Here $A_{A} = 2 A_{B}$ and $v_{A} = v_{B} = \sqrt{2 g h}$

$\Rightarrow$ $\frac{ρ_{A}}{ρ_{B}} = \frac{1}{2}$

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