  We study the motion of a rigid sphere falling in a two-layer stratified fluid
under the action of gravity in the potential flow regime. Experiments at a
moderate Reynolds number of approximately 20 to 450 indicate that a sphere with
the precise critical density, higher than the bottom layer density, can display
behaviors such as bounce or arrestment after crossing the interface. We
experimentally demonstrate that such a critical sphere density increases
linearly as the bottom fluid density increases with a fixed top fluid density.
Additionally, the critical density approaches the bottom layer fluid density as
the thickness of density transition layer increases. We propose an estimation
of the critical density based on the potential energy. With assuming the zero
layer thickness, the estimation constitutes an upper bound of the critical
density with less than 0.043 relative difference within the experimental
density regime 0.997 $g/cm^{3}$ $\sim $ 1.11 $g/cm^{3}$ under the zero layer
thickness assumption. By matching the experimental layer thickness, we obtain a
critical density estimation with less than 0.01 relative difference within the
same parameter regime.
