Two metallic rings and , identical in shape and size but having different resistivities and , are kept on top of two identical solenoids as shown in the figure. When current is switched on in both the solenoids in identical manner, the rings and jump

Question

Two metallic rings $A$ and $B$ , identical in shape and size but having different resistivities $ρ_{A}$ and $ρ_{B}$ , 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) [2009]

Smart Achievers · Accepted Answer

(2, 4)

Induced emf $B$ . For identical rings, the induced emf will be the same, but the currents will be different.

Given, $A$

Hence, $v_{A} > v_{B}$ as $(h = \frac{v^{2}}{2 g}) .$

If $ρ_{A} > ρ_{B},$ then $I_{A} < I_{B} .$ In this case, the given condition can be fulfilled if $m_{A} < m_{B} .$

If $ρ_{A} < ρ_{B},$ then $I_{A} > I_{B} .$ In this case, the given condition can be fulfilled if $m_{A} \leq m_{B} .$

Solution

1 $ρ_{A} > ρ_{B}$ and $m_{A} = m_{B}$

2 $ρ_{A} < ρ_{B}$ and $m_{A} = m_{B}$

3 $ρ_{A} > ρ_{B}$ and $m_{A} > m_{B}$

4 $ρ_{A} < ρ_{B}$ and $m_{A} < m_{B}$

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Solution

1 ρA>ρB and mA=mB

2 ρA<ρB and mA=mB

3 ρA>ρB and mA>mB

4 ρA<ρB and mA<mB

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1 $ρ_{A} > ρ_{B}$ and $m_{A} = m_{B}$

2 $ρ_{A} < ρ_{B}$ and $m_{A} = m_{B}$

3 $ρ_{A} > ρ_{B}$ and $m_{A} > m_{B}$

4 $ρ_{A} < ρ_{B}$ and $m_{A} < m_{B}$