A thin-walled container of mass $m$ floats vertically at the separation surface of the two liquids of density $ρ_1$ and $ρ_2$ . The whole mass of the container is concentrated in the part of height $h$.
The question is to determine the immersion depth $h'$of the container in the lower liquid if the bottom of the container has a thickness $h$ and an area $S$ and if the container itself is filled with the liquid of density $ρ_1$.
I applied the fundamental principle of the statics on the container
The weight of the container ($-mg$)
The buoyancy force applied by the fluid with density $ρ_2$ ($ρ_2gSh$)
The weight of the fluid with density $ρ_1$ (-$ρ_2gSh'$)
I summed up the forces and set them to zero and find my $h'$
but then realised that the fluid with density $ρ_1$ applied also a buoyoncy force on the top of the container , and the fluid with density $ρ_2$ applied a buoyoncy force on the other fluid.
Where's the problem ?