If a column of liquid 52 cm high supports a column of mercury ($\rho$ = 13.6 g/cm³)10 cm high,the density of the liquid is A)6.0 g/cm³ B)2.6 g/cm³ C)3.8 g/cm³ D)4.9 g/cm³ E)5.0 g/cm³

Question

Quizplus · Accepted Answer

The pressure exerted by both columns of liquid must be equal at the same depth. Using the formula for pressure $P = h \cdot \rho \cdot g$, where $h$ is the height of the liquid column, $\rho$ is the density, and $g$ is the acceleration due to gravity (which cancels out in this comparison), we can set the pressures equal to each other: $52 \cdot \rho_{liquid} = 10 \cdot 13.6$. Solving for $\rho_{liquid}$ gives $\rho_{liquid} = \frac{10 \cdot 13.6}{52} = 2.6 \, \text{g/cm}^3$.

If a Column of Liquid 52 Cm High Supports a Column