Which of the following statements about pressure in a liquid is correct?

Step 1: Analyze the question We need to find the one true statement about pressure in a liquid.

Step 2: The concept Pressure due to a liquid column is given by:

P = hρg

where h = depth, ρ = density of the liquid, g = acceleration due to gravity.

Key facts:

• Pressure increases with depth (h).
• Pressure increases with density (ρ).
• Pressure depends on g.
• Pressure at a point in a liquid acts equally in all directions.

Step 3: Check each option

• A. Pressure in a liquid increases with depth. True. Since P = hρg, P is directly proportional to h. This is why a dam wall is built thicker at the bottom.
• B. The higher the density, the lower the pressure. False. P is directly proportional to ρ, so a denser liquid (e.g. mercury) exerts more pressure than a less dense one (e.g. water) at the same depth.
• C. Pressure acts only perpendicular to the sides of the vessel. False. Pressure in a liquid acts in all directions at a point (up, down, and sideways). The force on a container wall is perpendicular to the wall, but the pressure itself is not restricted to that direction.
• D. Pressure is independent of g. False. g appears in P = hρg, so pressure depends on it. On the Moon, where g is smaller, the pressure at the same depth would be less.

Step 4: Answer The correct option is A.

Tip: Remember "hρg": every letter in it matters. If a statement says pressure is independent of h, ρ or g, or that it falls when they rise, it's wrong. Also remember that liquid pressure acts in all directions, a favourite WASSCE and JAMB trap.