Two metallic rings $A$ and $B$, identical in shape and sign but having different resistivities ${\rho }_A$ and ${\rho }_B$, are kept on top of two identical solenoids as shown in Fig. $9.79$. When current $I$ is switched on both the solenoids in identical manner, the rings $A$ and $B$ jumps to height $h_A>h_B$. The possible relation (s) between their resistances and their mass is (are)