Final answer:
The height of glycerin in a manometer measuring the same pressure as with water at 20 cm height would be 15.87 cm, due to glycerin's higher density of 1.26 g/cm³.
Step-by-step explanation:
When measuring the pressure of a gas with a manometer, the height of the liquid column is directly proportional to the gas pressure and inversely proportional to the density of the liquid used. Given that the height of water (density of 1 g/cm³) in the manometer is 20 cm, we can find the equivalent height if glycerin (density of 1.26 g/cm³) is used instead.
Using the formula P = h⋅ρ⋅g where P represents the pressure, h is the height, ρ is the density, and g is the acceleration due to gravity, the heights can be equated for water and glycerin since P and g remain constant for both situations. As a result, we get hwater⋅ρwater = hglycerin⋅ρglycerin. Hence, hglycerin = (hwater⋅ρwater)/ρglycerin which calculates to (20 cm ⋅ 1 g/cm³) / 1.26 g/cm³ = 15.87 cm. So the correct option for the height of glycerin in the manometer when measuring the same pressure is option b, 15.87 cm.