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AS · Practice questions · Density and pressure

Depth, density, upthrust.

Six original Cambridge-style questions on density, hydrostatic and total pressure, the depth formula, upthrust by Archimedes' principle, and floating fractions.

Original questions All questions on this page are original work, written in the Cambridge AS & A Level style. They are not from past papers. They test the same concepts and skills the syllabus rewards.
Keep these straight

Three formulas, used cleanly.

01
Analysis
[2 marks]

A metal cube of side 0.050 m has a mass of 1.0 kg. Find its density.

  • Volume = 0.050³ = 1.25 × 10⁻⁴ m³. ✓
  • ρ = m / V = 1.0 / (1.25 × 10⁻⁴) = 8000 kg m⁻³. ✓
02
Analysis
[2 marks]

Find the pressure exerted on the floor by a box of weight 600 N standing on a base of area 0.30 m².

  • p = F / A = 600 / 0.30 = 2000 Pa. ✓
03
Analysis
[3 marks]

Show that the extra pressure at a depth h in a liquid of density ρ is ρgh, by considering the weight of a column of liquid of cross-sectional area A.

  • A column of height h and area A has volume Ah, mass ρAh, and weight ρAhg. ✓
  • This weight presses on the area A at the base. ✓
  • Pressure = force / area = ρAhg / A = ρgh. ✓
04
Analysis
[3 marks]

A swimming pool is 2.5 m deep and filled with water of density 1000 kg m⁻³. Taking g = 9.8 m s⁻² and atmospheric pressure as 1.0 × 10⁵ Pa, find the total pressure at the bottom.

  • Hydrostatic pressure = ρgh = 1000 × 9.8 × 2.5 = 24 500 Pa. ✓
  • Total pressure = atmospheric + hydrostatic = 1.0 × 10⁵ + 0.245 × 10⁵. ✓
  • Total = 1.2 × 10⁵ Pa (to 2 significant figures). ✓
05
Analysis
[3 marks]

A block of volume 2.0 × 10⁻³ m³ is held fully submerged in water of density 1000 kg m⁻³ (g = 9.8 m s⁻²). Find the upthrust on it. If the block weighs 12 N, state whether it would float or sink when released.

  • Upthrust = ρgV = 1000 × 9.8 × 2.0 × 10⁻³ = 19.6 N. ✓
  • The maximum upthrust (19.6 N) is greater than the weight (12 N). ✓
  • So when released it rises and floats, settling with part of its volume above the surface. ✓
06
Analysis
[2 marks]

An iceberg of density 920 kg m⁻³ floats in seawater of density 1025 kg m⁻³. Find the fraction of the iceberg that is below the surface, and comment on the saying about an iceberg.

  • Submerged fraction = ρ_ice / ρ_sea = 920 / 1025 = 0.90. ✓
  • So about 90% is below the surface, and only about 10% shows, matching the idea of the hidden bulk of an iceberg. ✓

Mark this once you have attempted all six and checked your working. It records a Practiced badge on the topic and adds a one-time bonus. Revealing the solutions alone does not count.