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

We can use the equation for pressure:
P = 𝜌gh
where P is pressure, 𝜌 is density, g is acceleration due to gravity, and h is height.

For the column of liquid:
P = 𝜌LghL

For the column of mercury:
P = 𝜌MghM

Since the two columns are in equilibrium, the pressures are equal:
𝜌LghL = 𝜌MghM

Solving for 𝜌L, we get:
𝜌L = 𝜌MghM / ghL

Substituting the given values, we get:
𝜌L = (13.6 g/cm³)(10 cm) / (9.81 m/s²)(0.52 m)
𝜌L = 2.57 g/cm³

Therefore, the correct answer is B, 2.6 g/cm³.

If a Column of Liquid 52 Cm High Supports a Column