Answer
We can rank the plots according to the magnitude of the buoyant force on the bead:
$a \gt b \gt c$
Work Step by Step
The buoyant force is $~~F_b = m_f~g$
where $m_f$ is the mass of the fluid that has been displaced.
When the bead is submerged, the volume of liquid that is displaced is equal in all three cases.
If $p_g$ is greater for each depth $h$, then the liquid has a greater density.
Thus $a$ has the greatest density and $c$ has the smallest density.
Then, since the volume of liquid that is displaced is equal in all three cases, the amount of liquid $a$ that is displaced has the greatest mass, and the amount of liquid $c$ that is displaced has the smallest mass.
We can rank the plots according to the magnitude of the buoyant force on the bead:
$a \gt b \gt c$
