The density of water is 1.0 g/cm³. The density of the oil in the left column of the U-tube shown below is: A) 0.20 g/cm³ B) 0.80 g/cm³ C) 1.0 g/cm³ D) 1.3 g/cm³ E) 5.0 g/cm³

Question

Quizplus · Accepted Answer

The height difference between the two columns is 10 cm. The pressure difference between the two columns is given by the difference in the heights of the columns multiplied by the density of water (since water is the common liquid in the two columns) multiplied by the acceleration due to gravity (g = 9.8 m/s2 or 980 cm/s2). Using the equation P = ρgh, we find that the pressure difference is:
P = (1.0 g/cm3) x (10 cm) x (980 cm/s2) = 9.8 x 103 dynes/cm2
Because the pressure at the bottom of the U-tube is the same on both sides (due to the hydrostatic equilibrium), the pressure in the oil column must be equal to the pressure in the water column plus the pressure difference. Therefore, the pressure in the oil column is:
P = (1.0 g/cm3) x (20 cm) x (980 cm/s2) + 9.8 x 103 dynes/cm2 = 2.0 x 104 dynes/cm2
The density of the oil can be found by using the equation P = ρgh for the oil column:
2.0 x 104 dynes/cm2 = ρ x g x h
where h is the height of the oil column. Solving for ρ, we get:
ρ = 2.0 x 104 dynes/cm2 / (g x h) = 2.0 x 104 dynes/cm2 / (980 cm/s2 x 10 cm) = 2.04 g/cm3
Therefore, the density of the oil is 2.04 g/cm3, which is closest to 0.80 g/cm3 (choice B).

The Density of Water Is 1