1) Same object, different density of medium
The same object here is the single ship. Let's analyze the question outline:
- Everything is similar in the Trinity (my term) (weight = buoyancy = water displaced) regardless the medium.
- Only volume of submerged part is different (the dark-blue part)
2) Different objects, same density of medium
The objects differ weight. Let's analyze the question outline:
- The Trinity is SIMILAR in an object (weight = buoyancy = water displaced)
- The Trinity is DIFFERENT between objects (because of different weight laa...)
- Of course, the volume of submerged part is different...
Now you can already answer the question regarding Archimedes Principle. Hope to give you more later!