Equal volumes of two immiscible liquids of density 2 ρ and 4 ρ , respectively, are filled in the vessel as shown in the figure. Two small holes are punched at depth h 2 and 2 h , respectively, from th

Question

Equal volumes of two immiscible liquids of density $2 ρ$ and $4 ρ$ , respectively, are filled in the vessel as shown in the figure. Two small holes are punched at depth $\frac{h}{2}$ and $2 h$ , respectively, from the surface of the lighter liquid. If $v_{1}$ and $v_{2}$ are the velocities of efflux at these holes, then the ratio of $\frac{v_{1}}{v_{2}}$ is

TestHub · Accepted Answer

2 ρ g h 2 = 1 2 2 ρ v 1 2 ⇒ v 1 = g h 4 ρ g h + 2 ρ g h = 1 2 ⋅ 4 ρ v 2 2 ⇒ 6 ρ g h = 2 ρ v 2 2 ⇒ v 2 = 3 g h ∴ v 1 v 2 = 1 3

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