Archimedes’ principle says the buoyant force on an object equals the weight of the fluid it displaces. The formula is F = ρVg, where ρ is the fluid density and V is the submerged volume.
This lesson is part of SPM Physics pressure. It uses the depth idea from comparing pressure at different depths.
Why does a liquid push up on an object?
The bottom of a submerged object is deeper than its top, so the pressure pushing up is larger than the pressure pushing down. The difference is the upward buoyant force.
An object sinks when its weight is greater than the buoyant force. It floats when the two are equal, and in that case the object displaces exactly its own weight of fluid.
Worked example: a block fully under water
An original block has a volume of 0.0020 m³ and a mass of 5.0 kg. It is held fully under water (ρ = 1000 kg m⁻³).
Buoyant force = 1000 × 0.0020 × 10 = 20 N. Weight = 5.0 × 10 = 50 N. The weight is greater, so the block sinks, and the net downward force is 50 − 20 = 30 N.
Worked example: a floating block
A wooden block of mass 0.60 kg floats in water. Its weight is 6.0 N, so the buoyant force is also 6.0 N.
The displaced volume is V = F ÷ (ρg) = 6.0 ÷ (1000 × 10) = 6.0 × 10⁻⁴ m³, which is 600 cm³. If the block has a total volume of 1000 cm³, then 600 cm³ is underwater and 400 cm³ is above it.
The mistake that costs marks
The common slip is to use the whole volume of the block in a floating question.
| Step | Wrong | Right |
|---|---|---|
| Volume in ρVg | 1000 cm³ (whole block) | 600 cm³ (submerged part) |
| Buoyant force | 10 N | 6.0 N |
| Conclusion | Buoyant force exceeds weight | Buoyant force equals weight |
The wrong answer predicts the block should rise out of the water, which contradicts the fact that it floats. Always ask whether the object is fully or only partly submerged.
How do I use apparent weight?
A spring balance shows the apparent weight of an object in a liquid. Apparent weight = actual weight − buoyant force.
An original stone reads 8.0 N in air and 5.0 N when fully in water. The buoyant force is 3.0 N, so the stone’s volume is 3.0 ÷ (1000 × 10) = 3.0 × 10⁻⁴ m³. Its mass is 8.0 ÷ 10 = 0.80 kg, so the density is 0.80 ÷ (3.0 × 10⁻⁴) ≈ 2.7 × 10³ kg m⁻³.
Check yourself
An original object of weight 12 N hangs from a spring balance and is fully immersed in oil of density 800 kg m⁻³. The balance reads 8.0 N. Find the volume of the object.
Answer
Buoyant force = 12 − 8.0 = 4.0 N.
V = F ÷ (ρg) = 4.0 ÷ (800 × 10) = 5.0 × 10⁻⁴ m³, which is 500 cm³.
The object is fully immersed, so this is its whole volume.
What to study next
Buoyancy explains floating in liquids; the last lesson handles moving fluids, where pressure changes for a different reason. Continue with explaining fluid-flow effects, then try the pressure practice set.
For guided practice with floating and sinking questions, see online one-to-one Physics tuition.