Question
A wooden solid cylinder (density $0.80\text{ }kg/m^{3}$ ), a plastic ball (density $0.90\text{ }kg/m^{3}$ ) and a rubber cube (density $0.95\text{ }kg/m^{3}$ ) all of equal mass M float partly immersed in a through containing water (density $1.00\text{ }kg/m^{3}$ ) as shown below (ignore any tilt during floatation)
You may conclude that
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Solution
Sol. Key concept: Floating equilibrium and Archimedes’ principle.
Each object floats at rest, so the upward buoyant force equals its weight. All three objects have the same mass M and hence the same weight Mg, irrespective of their shapes or densities.
$$F_{B} = \rho_{water}gV_{displaced} = Mg$$
The displaced water volume is therefore the same for all three. Their total volumes and immersed fractions differ, but the buoyant forces do not. Hence (d).
Correction / clarification: The numerical densities in the stem correspond to g cm⁻³ (or to 800, 900, 950 and 1000 kg m⁻³), not to the printed kg m⁻³ values. This unit issue does not change the equal-force conclusion.
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