NDA (I & II) 2020 General Ability Test · Question 74 of 148

Correct — B, the pressure depends on the height of the liquid column. Pressure at the base of a liquid is P = h x rho x g, where h is the height (depth) of the liquid, rho its density and g the acceleration due to gravity. So the pressure rises with the height of the column and with the liquid's density, but it does not depend on the area of the base or the shape of the vessel.

• (a)The pressure depends on the area of the base of the beaker — Pressure (force per unit area) is independent of the base area; a wider beaker holds more liquid, but the pressure at a given depth is the same.
• (c)The pressure does not depend on the density of the liquid — This is false; P = h x rho x g increases with density, so a denser liquid exerts more pressure at the same depth.
• (d)The pressure neither depends on the area of the base of the beaker nor on the height of liquid column — The pressure does depend on the height (and density); only the base area is irrelevant, so this statement is wrong.

Hydrostatic pressure at a depth h in a liquid is P = h x rho x g. It depends only on depth, density and gravity — not on the container's cross-sectional area or shape. This surprising independence from shape is called the hydrostatic paradox.

The tempting error is to think a bigger base or more liquid means more pressure. Isolate the variables in P = h x rho x g: only depth and density matter for the pressure itself.

• Pressure at depth h in a liquid is P = h x rho x g.
• It increases with depth and with density.
• It is independent of the base area or the shape of the container (hydrostatic paradox).
• The total force on the base equals pressure multiplied by area, so force does depend on area even though pressure does not.

• Confusing pressure (independent of area) with total force (which equals pressure multiplied by area).
• Thinking a wider or larger container means higher pressure at the same depth.

Asked by asking what the pressure at the base of a liquid column does or does not depend on.

No directly related past PYQ was found.

• practice — not a real PYQ

  The pressure exerted by a liquid at a point inside it depends on

  • (a)the shape of the container
  • (b)the depth below the surface
  • (c)the area of the base
  • (d)the total volume of liquid

  Answer(b) the depth below the surface (along with density and gravity).

• practice — not a real PYQ

  Two vessels of different shapes are filled with water to the same height. The pressure at the base is

  • (a)greater in the wider vessel
  • (b)greater in the narrower vessel
  • (c)the same in both
  • (d)zero in both

  Answer(c) the same in both — the hydrostatic paradox.