Two metallic rings $A$ and $B$, identical in shape and size but having different resistivities $\rho_A \, and \, \rho_B$, are kept on top of two
identical solenoids as shown in the figure. When current $I$ is switched on in both the solenoids in identical manner, the rings $A$ and $B$ jump to heights $h_A \, and \, h_B$, respectively, with $h_A > h_B$. The possible relation(s) between their resistivities and their masses $m_A$ and $m_B$ is (are)