Equal volume of two immiscible liquids of densities and 2 ρ are filled in a vessel as shown in figure. Two small holes are punched at depths (h/2) and (3 h/2) from the surface of lighter liquid. If v1 and v2 are the velocities of efflux at these two holes, then (v1/v2) is

Question

Equal volume of two immiscible liquids of densities and 2 ρ are filled in a vessel as shown in figure. Two small holes are punched at depths (h/2) and (3 h/2) from the surface of lighter liquid. If v1 and v2 are the velocities of efflux at these two holes, then (v1/v2) is <img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/physics/c3ce318da8a006c1fc3d10863199f839-.png" /> (A) (1/2 √2) (B) (1/2) (C) (1/4) (D) (1/√2)

Tardigrade Admin · Accepted Answer

v1=√2 g((h/2))=√g h Using Bernoulli's theorem, we get Pa+ρ g h+2 ρ g((h/2)) =Pa+(1/2)(2 ρ) v22 or v2=√2 g h ∴ (v1/v2)=(1/√2)

$\frac{1}{2 2}$

$\frac{1}{2}$

$\frac{1}{4}$

$\frac{1}{2}$

$v_{1} = 2 g (\frac{h}{2}) = g h$
Using Bernoulli's theorem, we get
$P_{a} + ρ g h + 2 ρ g (\frac{h}{2})$
$= P_{a} + \frac{1}{2} (2 ρ) v_{2}^{2}$ or $v_{2} = 2 g h$
$∴ \frac{v _{1}}{v _{2}} = \frac{1}{2}$

Q. Equal volume of two immiscible liquids of densities and 2ρ are filled in a vessel as shown in figure. Two small holes are punched at depths 2h​ and 23h​ from the surface of lighter liquid. If v1​ and v2​ are the velocities of efflux at these two holes, then v2​v1​​ is

22​1​

21​

41​

2​1​

v1​=2g(2h​)​=gh​ Using Bernoulli's theorem, we get Pa​+ρgh+2ρg(2h​) =Pa​+21​(2ρ)v22​ or v2​=2gh​ ∴v2​v1​​=2​1​

$\frac{1}{2 2}$

$\frac{1}{2}$

$\frac{1}{4}$

$\frac{1}{2}$

$v_{1} = 2 g (\frac{h}{2}) = g h$
Using Bernoulli's theorem, we get
$P_{a} + ρ g h + 2 ρ g (\frac{h}{2})$
$= P_{a} + \frac{1}{2} (2 ρ) v_{2}^{2}$ or $v_{2} = 2 g h$
$∴ \frac{v _{1}}{v _{2}} = \frac{1}{2}$