Two metallic rings $\mathrm{A}$ and $\mathrm{B}$, 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 $\mathrm{A}$ and $\mathrm{B}$ 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)
$(A)$ $\rho_A>\rho_B$ and $m_A=m_B$
$(B)$ $\rho_A<\rho_B$ and $m_A=m_B$
$(C)$ $\rho_A>\rho_B$ and $m_A > m_B$
$(D)$ $\rho_A<\rho_B$ and $m_A < m_B$
