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  4. Two chemically non-reactive liquids are placed in a U -shaped tube as shown in the figure. The height of any liquid above a common reference line is <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-a0yowotao1i7gkjq.jpg />

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Q. Two chemically non-reactive liquids are placed in a $U$ -shaped tube as shown in the figure. The height of any liquid above a common reference line is
Question

NTA AbhyasNTA Abhyas 2022

Solution:

The pressure at the common reference must be the same, for both the liquids. Since both tubes are open to the atmosphere, we must have
$h_{1}\rho _{1}g=h_{2}\rho _{2}g$
$\Rightarrow h_{1}\rho _{1}=h_{2}\rho _{2}$
$\Rightarrow h\rho =constant$
$\Rightarrow h \propto \frac{1}{\rho }$