A container of large uniform cross-sectional area A is resting on… - Vidyadip

MCQ

A container of large uniform cross-sectional area $A$ is resting on a horizontal surface holds two immiscible, non-viscous and incompressible liquids of densities $d$ and $2d$ each of height $\frac{H}{2}$ as shown. The lower density of liquid is open to atmosphere. A small hole is made on the wall of container at height $h\left( {h < \frac{H}{2}} \right)$. The initial speed of efflux of the liquid at the hole is

A
$\left( {3H - 4h} \right)g$
B
$\frac{{\left( {3H - 4h} \right)g}}{2}$
C
$\sqrt {\left( {3H - 4h} \right)g} $
✓
$\sqrt {\frac{{\left( {3H - 4h} \right)g}}{2}} $

✓

Answer

Correct option: D.

$\sqrt {\frac{{\left( {3H - 4h} \right)g}}{2}} $

d
Applying Bemoulli theorem between points $1$ and $2$

$\mathrm{p}_{0}+\frac{\mathrm{H}}{2} \rho \mathrm{dg}+\left(\frac{\mathrm{H}}{2}-\mathrm{h}\right) 2 \mathrm{dg}=\mathrm{p}_{0}+\frac{1}{2}(2 \mathrm{d}) \mathrm{v}^{2}$

solving $v=\sqrt{\frac{(3 \mathrm{H}-4 \mathrm{h}) \mathrm{g}}{2}}$

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