Question

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)

• A. $\rho_A > \rho_B$ and $m_A = m_B$
• B. $\rho_A
• C. $\rho_A >\, \rho_B$ and $m_A >\, m_B$
• D. $\rho_A < \rho_B$ and $m_A < m_B$

Answer 1

Answer: (D)

$\rho_A < \rho_B$ and $m_A < m_B$

Answer 2

Induced emf $e = - \frac{d \phi }{dt}$. For identical rings induced emf will
be same. But currents will be different. Given $h_A > h_B$.
Hence, $v_A > v_B \, as \bigg( h = \frac{v^2}{2g}\bigg).$
If $\rho_A > \rho_B$, then, $I_A < I_B$. In this case given condition can be
fulfilled if $m_A < m_B$.
If $\rho_A < \rho_B$, then $I_A > I_B$. In this case given condition can be
fulfilled if $m_A \le m_B$