Consider two liquids $\mathrm{A}$ and $\mathrm{B}$ in a U-shaped tube in static equilibrium as shown in the…

Consider two liquids $\mathrm{A}$ and $\mathrm{B}$ in a U-shaped tube in static equilibrium as shown in the figure. If the density of the liquid $A$ is twice the density of liquid $B$, then the relation between $h_A$ and $h_B$ is
  1. $\mathrm{h}_{\mathrm{A}}=\frac{\mathrm{h}_{\mathrm{B}}}{\sqrt{2}}$
  2. $\mathrm{h}_{\mathrm{A}}=\frac{\mathrm{h}_{\mathrm{B}}}{2}$
  3. $\mathrm{h}_{\mathrm{A}}=\frac{\mathrm{h}_{\mathrm{B}}}{3}$
  4. $\mathrm{h}_{\mathrm{A}}=\frac{\mathrm{h}_{\mathrm{B}}}{\sqrt{3}}$

Solution

We have $ \begin{aligned} & \mathrm{P}_0+\rho_{\mathrm{A}} \mathrm{gh}_{\mathrm{A}}=\mathrm{P}_0+\rho_{\mathrm{B}} \mathrm{gh}_{\mathrm{B}} \\ & \Rightarrow 2 \rho_{\mathrm{B}} \mathrm{gh}_{\mathrm{A}}=\rho_{\mathrm{B}} \mathrm{gh}_{\mathrm{B}} \\ & \Rightarrow \mathrm{h}_{\mathrm{A}}=\frac{\mathrm{h}_{\mathrm{B}}}{2} \end{aligned} $

Asked in: AP EAMCET 2022 (06 Jul Shift 1)

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