Equal volumes of two immiscible liquids of densities and 2 are fi… - Vidyadip

MCQ

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
$\frac{1}{4}$
✓
$\frac{1}{{\sqrt 2 }}$

✓

Answer

Correct option: D.

$\frac{1}{{\sqrt 2 }}$

d
We have $v_{1}=\sqrt{2 g h(h / 2)}=\sqrt{g h} \ldots . .(i)$

and by using Bernoulli's theorem

$\rho g h+2 \rho g\left(\frac{h}{2}\right)=\frac{1}{2}(2 \rho) v_{2}^{2}$

$\Rightarrow v_{2}=\sqrt{2} g h \ldots . .(i i)$

From Eqs. $(i)$ and $(ii)$

$\frac{v_{1}}{v_{2}}=\frac{1}{\sqrt{2}}$

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