JEE Advanced · Physics · 20. Magnetism & Current
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 \(\rho_A < \rho_B\) and \(m_A=m_B\)
- C \(\rho_A>\rho_B\) and \(m_A>m_B\)
- D \(\rho_A < \rho_B\) and \(m_A < m_B\)
Answer & Solution
Correct Answer
(D) \(\rho_A < \rho_B\) and \(m_A < m_B\)
Step-by-step Solution
Detailed explanation
Induced emf \(e=-\frac{d \phi}{d t}\). For identical rings induced emf will be same. But currents will be different. Given \(h_A>h_B\). Hence, \(v_A>v_B\) as \(\left(h=\frac{v^2}{2 g}\right)\).
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 of \(m_A \leq m_B\).
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 of \(m_A \leq m_B\).
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