Buoyant Force in High vs Low Density Liquids: Homework Statement & Solution

[chetzread]

is there anything to do with the metacentric height , buoyant point in this question ?

 

[haruspex]

is there anything to do with the metacentric height , buoyant point in this question ?

Not specifically. I just wanted to alert you to the fact that the topic is subtler than may appear, that it might not actually be true that the object would always be more stable in the lighter fluid, and that even if it is a rigorous proof would not be easy.