Question

Question:Rank the buoyant forces exerted on the following five objects of equal volume from the largest to the smallest. Assume the objects have been dropped into a swimming pool and allowed to come to mechanical equilibrium. If any buoyant forces are equal, state that in your ranking. (a) a block of solid oak (b) an aluminum block (c) a beach ball made of thin plastic and inflated with air (d) an iron block (e) a thin-walled, sealed bottle of water.

Short answer

Option (a), (b), (c), (d), and (e) will experience the highest buoyant force. So they all experience the same buoyant force.

Step-by-step solution

Step 1: Archimedes’ principle

When an object is partially or fully submerged in a fluid, the fluid exerts on the object an upward force called the buoyant force. According to Archimedes’s principle, the magnitude of the buoyant force is equal to the weight of the fluid displaced by the object:

B =${\rho }_{Fluid}g{V}_{disp}$

Where V_dispthe volume of fluid is displaced and ${\rho }_{Fluid}$is the density of the fluid.

State the ranking

The buoyant force acting on a submerged object only depends on the displaced volume. Since (a), (b), (c), (d), and (e) all have the same volume; they will displace the same volume of liquid. So they all experience the same buoyant force. So (a), (b), (c), (d), and (e) will experience the highest buoyant force.

The volume of an object is directly related to its mass and density by:

$\rho =\frac{M}{V}\left(or\right)v=\frac{M}{\rho }$

Since the buoyant force acting on a submerged object only depends on the displaced volume, you can conclude that the buoyant force depends on the ratio of the object’s mass to the density of the object ($\frac{M}{\rho }$ )