The density of water is 1.0 g/cm³. If h = 20 cm, the density of the oil in the left column of the U-tube shown below is: A) 0.20 g/cm³ B) 0.90 g/cm³ C) 1.0 g/cm³ D) 1.3 g/cm³ E) 5.0 g/cm³

Question

Quizplus · Accepted Answer

In a U-tube, the pressure at the same height on both sides of the tube is the same. Hence, the pressure at point A of the oil column is the same as the pressure at point B of the water column. 
We can use the formula:
pressure = density x gravity x height
Let the density of the oil be x g/cm³.
At point B: 
pressure = 1.0 g/cm³ x 9.8 m/s² x 20 cm = 196 g/cm²/s²
At point A: 
pressure = x g/cm³ x 9.8 m/s² x h 
196 g/cm²/s² = x g/cm³ x 9.8 m/s² x h
x = 196 g/cm²/s² ÷ (9.8 m/s² x 20 cm) 
x = 0.999 ≈ 0.90 g/cm³ 
Therefore, the density of the oil in the left column of the U-tube is 0.90 g/cm³, which corresponds to choice B.

The Density of Water Is 1