Density and upthrust

Density

ρ = m / V, measured in kg/m³. To convert from g/cm³ to kg/m³, multiply by 1000 (water is 1.00 g/cm³ = 1000 kg/m³). Remember 1 cm³ = 10^-6 m³.

Upthrust

An object in a fluid feels an upward force called upthrust. Upthrust is equal to the weight of fluid displaced (Archimedes' principle). For a fully submerged object of volume V: upthrust = ρ_fluid x V x g.

Floating and sinking

• An object floats when the upthrust equals its weight; it sinks until it displaces its own weight of fluid.
• If the weight is greater than the largest possible upthrust (fully submerged), it sinks.
• The 'apparent weight' of a submerged object = weight - upthrust.

Worked example

A block of volume 0.0020 m³ is fully submerged in water of density 1000 kg/m³. Find the upthrust.

1. Mass of water displaced = 1000 x 0.0020 = 2.0 kg
2. Weight of water displaced = 2.0 x 9.81

Answer: Upthrust = 19.6 N

Check yourself

1. A 540 g object has a volume of 200 cm³. Find its density in kg/m³.
   Show answer

   2700 kg/m³. ρ = 540 / 200 = 2.7 g/cm³ = 2700 kg/m³.

2. Find the mass of 0.50 m³ of oil of density 920 kg/m³, in kg.
   Show answer

   460 kg. m = ρV = 920 x 0.50 = 460 kg.

3. A stone of volume 5.0 x 10^-4 m³ is fully submerged in water (density 1000 kg/m³). Find the upthrust in N, to 3 s.f.
   Show answer

   4.91 N. Upthrust = 1000 x 5.0 x 10^-4 x 9.81 = 4.91 N.

4. The stone in the last question weighs 15.0 N in air. What does it appear to weigh when fully submerged in water, in N? Give 3 s.f.
   Show answer

   10.1 N. Apparent weight = 15.0 - 4.905 = 10.1 N.

5. A 0.60 kg wooden block floats in water (density 1000 kg/m³). What volume of water does it displace, in cm³?
   Show answer

   600 cm³. It displaces its own weight: 0.60 kg of water, which is 0.60 / 1000 = 6.0 x 10^-4 m³ = 600 cm³.

6. An object floats at rest on water. How does the upthrust compare with its weight?
   • Upthrust is greater
   • Upthrust is smaller
   • Upthrust is zero
   • They are equal
   Show answer

   They are equal. It is in equilibrium, so the resultant force is zero.

7. The upthrust on an object in a fluid is equal to
   • its own weight
   • the weight of fluid it displaces
   • its mass x g
   • the density of the fluid
   Show answer

   the weight of fluid it displaces. This is Archimedes' principle, as stated in the specification.

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Sources

• Pearson Edexcel International Advanced Subsidiary/Advanced Level in Physics specification (XPH11/YPH11), Issue 3
• Pearson qualifications: International Advanced Levels Physics (2018)
• Pearson Edexcel IAL Physics Unit 1 (WPH11) question paper, January 2023: list of data (g = 9.81 m/s²)

Last updated 7 November 2026. Spotted a mistake? Tell us.