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

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" /> (A) Directly proportional to their densities (B) Inversely proportional to their densities (C) Directly proportional to square of their densities (D) Equal

Tardigrade Admin · Accepted Answer

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} ρ_{1} g = h_{2} ρ_{2} g

\Rightarrow h_{1} ρ_{1} = h_{2} ρ_{2}

\Rightarrow h ρ = co n s t an t

\Rightarrow h \propto \frac{1}{ρ}

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

Directly proportional to their densities

Inversely proportional to their densities

Directly proportional to square of their densities

Equal

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 h1​ρ1​g=h2​ρ2​g ⇒h1​ρ1​=h2​ρ2​ ⇒hρ=constant ⇒h∝ρ1​

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

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
$h_{1} ρ_{1} g = h_{2} ρ_{2} g$
$\Rightarrow h_{1} ρ_{1} = h_{2} ρ_{2}$
$\Rightarrow h ρ = co n s t an t$
$\Rightarrow h \propto \frac{1}{ρ}$