I. Density of the liquid. II. Depth below the surface of the liquid. III. Surface area of the liquid. In which…

Analyze the question: The question asks which of the factors (density, depth, surface area) the pressure in a liquid depends on.

Concept: Pressure at a point in a liquid at rest is given by:

P = hρg

where

• h = depth below the surface of the liquid
• ρ = density of the liquid
• g = acceleration due to gravity (constant at a given place)

(If atmospheric pressure acts on the surface, we add it: P = P₀ + hρg. It is still independent of area.)

Solution:

• I. Density of the liquid: P is directly proportional to ρ. A denser liquid, such as mercury, gives more pressure than water at the same depth. Yes, it depends.
• II. Depth below the surface: P is directly proportional to h. The deeper you go, the greater the pressure. Yes, it depends.
• III. Surface area of the liquid: The area does not appear in the formula. Pressure is force per unit area, and when the area changes, the force changes in proportion, so the pressure stays the same. A wide lake and a narrow tube of water have the same pressure at the same depth. No, it does not depend.

So pressure depends on I and II only.

Exam tip: Remember "hρg", which contains depth and density but no area. Whenever a question asks what liquid pressure depends on, rule out area, shape of the container, and volume of the liquid. These are common distractors in JAMB.