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. ${\rho }_A<{\rho }_B$ 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 1

Answer: (B), (D)

${\rho }_A<{\rho }_B$ and $m_A=m_B$
${\rho }_A<{\rho }_B$ and $m_A<m_B$

As $-\frac{d\varphi }{dt}=emf$ is same, the current induced in the ring will depend upon resistance of the ring. Larger the resistivity smaller the current.
If $m_A=m_B$ and ${\rho }_A<{\rho }_B$, current in ring A will be more and it will experience more force than ring B. Therefore ring A would go to a higher height.
If $m_A<m_B$ and ${\rho }_A<{\rho }_B$, current in ring A will be more and it will experience more force than ring B. Ring A also being lighter in mass, it would go to a higher height than ring B.