A liquid of density ρ is in a container with bottom area S. How much will the level of that liquid rise in the container if we throw a non-sinking object of mass m into the container?

Question

A liquid of density ρ is in a container with bottom area S. How much will the level of that liquid rise in the container if we throw a non-sinking object of mass m into the container?

Answer 1

Draw a sketch.

The free body diagram shows the weight of the object (W) is pulling down while the buoyancy force (F_B) is pushing up.

The weight is calculated as W = mg

The buoyancy force is the weight of the displaced liquid. F_B = Vρg (where V is the volume of the displaced liquid)

Since the object is floating then W = F_B or mg = Vρg which simplifies to m = Vρ or V = m/ρ

If V is the volume of the displaced liquid, then the liquid rose by that volume. The volume of liquid = area of the base times the height = S•h so S•h = m/ρ therefore h (the amount the level of the liquid rose) = m/(Sρ)