The pressure at any point in a liquid at rest depends only on the

Analyze the question: It asks which quantities determine the pressure at a point inside a liquid that is at rest (a hydrostatic situation).

Explain the concept: The pressure due to a liquid column is given by:

P = hρg

where:

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

(If the liquid is open to the air, atmospheric pressure is added: P = P₀ + hρg. Even then, the liquid's contribution depends only on depth and density.)

Solution:

• Pressure depends on depth (h) and density (ρ), and g is constant.
• It does not depend on the shape of the container, the total quantity or mass of liquid, or the surface area. This is why a narrow tube and a wide tank filled to the same depth with the same liquid give the same pressure at the bottom.
• Viscosity matters only when a fluid is moving. In a liquid at rest it plays no role.

Checking the options:

• A. Depth and density: correct, matches P = hρg.
• B. Mass and volume: these only matter through density, and they are not the direct factors. A large volume at small depth gives low pressure.
• C. Quantity and surface area: pressure does not depend on these.
• D. Surface area and viscosity: neither affects hydrostatic pressure.

Answer: A

Exam tip: Remember "hρg": pressure in a liquid at rest depends on height (depth) and ρ (density), with g constant. If an option mentions shape, total volume, surface area, or viscosity, it is almost certainly a distractor for hydrostatic pressure questions.