A cylindrical oceanographic probe of mass \(M\), height \(H\), and uniform cross-sectional area \(A\) floats vertically across the horizontal boundary between two immiscible seawater layers. The upper layer has density \(\rho_1\) and the lower layer has density \(\rho_2\), where \(\rho_1 < \rho_2\). A warm plume from a hydrothermal vent reduces the density of the upper layer to a lower value \(\rho_1'\), while the density \(\rho_2\) of the lower layer remains unchanged. Which of the following claims correctly describes the change in the depth \(h_2\) of the probe submerged in the lower layer, and provides the correct physical justification?