Question

Two identical tanks contain water and a liquid of density 0.8 g/cm ³. Pressure exerted by the liquid is equal to the pressure due to water column of 50 cm. Find the height of the liquid column in the tank?

Answer 1

Given,
Density of liquid, ρ' = 0.8 g/cm ³ = 800 kg/m³
Density of water, ρ = 1000 kg/m³

Pressure due to water column of 50 cm is given by
$$\begin{gathered} P=\rho gh \\ P=1000\times 9.8\times 0.5 \\ =4900\mathrm{pa} \end{gathered}$$
Let P' be the pressure due to height of the liquid column in the tank. Now according to question
$$\begin{gathered} P\text{'}=P \\ \Rightarrow \rho \text{'}g{h}_1=4900 \\ \Rightarrow h_1=\frac{4900}{800\times 9.8} \\ \Rightarrow h_1=0.625\mathrm{m} \end{gathered}$$