Equal volumes of two immiscible liquids of density 2ρ and 4ρ , respectively, are filled in the vessel as shown in the figure. Two small holes are punched at depth (h/2) and 2h , respectively, from the surface of the lighter liquid. If v1 and v2 are the velocities of efflux at these holes, then the ratio of (v1/v2 ) is

Question

Equal volumes of two immiscible liquids of density 2ρ and 4ρ , respectively, are filled in the vessel as shown in the figure. Two small holes are punched at depth (h/2) and 2h , respectively, from the surface of the lighter liquid. If v1 and v2 are the velocities of efflux at these holes, then the ratio of (v1/v2 ) is <img class="img-fluid question-image" alt="Question" src="https://cdn.tardigrade.in/q/nta/p-ed4jtgjcajmz.png" /> (A) 1/3 (B) 1/√3 (C) 1/2 (D) 1/√2

Tardigrade Admin · Accepted Answer

2ρ g(h/2)=(1/2)2ρ v12 ⇒ v1=√g h 4ρ gh+2ρ gh=(1/2)⋅ 4ρ v22 ⇒ 6ρ gh=2ρ v22 ⇒ v2=√3 g h ∴ (v1/v2)=(1/√3)

$1/3$

$1/ 3$

$1/2$

$1/ 2$

$2 ρ g \frac{h}{2} = \frac{1}{2} 2 ρ v_{1}^{2} \Rightarrow v_{1} = g h$
$4 ρ g h + 2 ρ g h = \frac{1}{2} \cdot 4 ρ v_{2}^{2}$
$\Rightarrow 6 ρ g h = 2 ρ v_{2}^{2} \Rightarrow v_{2} = 3 g h$
$∴ \frac{v _{1}}{v _{2}} = \frac{1}{3}$

1/3

1/3​

1/2

1/2​

2ρg2h​=21​2ρv12​⇒v1​=gh​ 4ρgh+2ρgh=21​⋅4ρv22​ ⇒6ρgh=2ρv22​⇒v2​=3gh​ ∴v2​v1​​=3​1​

$1/3$

$1/ 3$

$1/2$

$1/ 2$

$2 ρ g \frac{h}{2} = \frac{1}{2} 2 ρ v_{1}^{2} \Rightarrow v_{1} = g h$
$4 ρ g h + 2 ρ g h = \frac{1}{2} \cdot 4 ρ v_{2}^{2}$
$\Rightarrow 6 ρ g h = 2 ρ v_{2}^{2} \Rightarrow v_{2} = 3 g h$
$∴ \frac{v _{1}}{v _{2}} = \frac{1}{3}$