Weight Equals Buoyancy: Read the Fraction Submerged
Every buoyancy question uses Archimedes' principle: the upthrust equals the weight of fluid displaced. A floating body satisfies weight = upthrust, which turns most problems into a density ratio.
Chemistry questions first require the material, particles or reaction condition to be identified before a formula or rule is selected.
Floating means weight equals upthrust
An 800 g cube of edge 10 cm has density 0.8 g/cm³, so 80% of it is submerged and 200 cm³ is outside the water. A sphere with 2/3 of its volume outside water has density 1/3 g/cm³;
Apparent weight and bodies at rest at an interface
A fully submerged object of weight W and density ρ in a fluid of density ρ1 displaces a weight W ρ1/ρ of fluid, so its apparent weight is W(1 - ρ1/ρ). A ball that comes to rest at the boundary between two non-mixing liquids is denser than the upper liquid and less dense than the lower one, so ρ_upper < ρ_ball < ρ_lower. When a block hangs from a spring balance inside a beaker on another balance, the spring balance reads less by exactly the upthrust and the beaker balance reads more by the same amount, so the total of the two readings stays constant.
Changing loads and released bodies
If a coin on a floating block falls into the water, the block no longer carries the coin's weight, so it floats higher and displaces less water, while the coin displaces only its own small volume; the block rises and the water level in the container falls. A wooden block released at the bottom of a lake feels a constant upward net force (ρ_water - ρ_wood) V g, so, neglecting water drag, it rises with constant acceleration.
OlympIQ exam lens
- ✓Upthrust = ρ_fluid V_sub g; a floating body has weight = upthrust
- ✓Submerged fraction = ρ_body / ρ_fluid
- ✓Apparent weight = W (1 - ρ_fluid / ρ_body)
- ✓A ball resting at a liquid interface has ρ_upper < ρ_ball < ρ_lower
- ✓Spring-balance and beaker-balance readings change by equal and opposite amounts
Do not think a floating body displaces its own volume of fluid. It displaces only its submerged volume, whose weight equals the body's weight; the density ratio decides what fraction that is.
Ready to try the pattern?
100% coverage across the 12 linked questions.
Practise 12 linked questions