$A$ thin conducting rod $MN$ of mass $20 \text{ g}$,length $25 \text{ cm}$ and resistance $10 \text{ }\Omega$ is held on frictionless,long,perfectly conducting vertical rails as shown in the figure. There is a uniform magnetic field $B_0 = 4 \text{ T}$ directed perpendicular to the plane of the rod-rail arrangement. The rod is released from rest at time $t = 0$ and it moves down along the rails. Assume air drag is negligible. Match each quantity in List-$I$ with an appropriate value from List-$II$,and choose the correct option. [Given: The acceleration due to gravity $g = 10 \text{ m s}^{-2}$ and $e^{-1} = 0.4$]
List-$I$List-$II$
$(P)$ At $t = 0.2 \text{ s}$,the magnitude of the induced emf in Volt$(1)$ $0.07$
$(Q)$ At $t = 0.2 \text{ s}$,the magnitude of the magnetic force in Newton$(2)$ $0.144$
$(R)$ At $t = 0.2 \text{ s}$,the power dissipated as heat in Watt$(3)$ $1.20$
$(S)$ The magnitude of terminal velocity of the rod in $\text{m s}^{-1}$$(4)$ $0.12$
$(5)$ $2.00$

  • A
    $P \rightarrow 5, Q \rightarrow 2, R \rightarrow 3, S \rightarrow 1$
  • B
    $P \rightarrow 3, Q \rightarrow 1, R \rightarrow 4, S \rightarrow 5$
  • C
    $P \rightarrow 4, Q \rightarrow 3, R \rightarrow 1, S \rightarrow 2$
  • D
    $P \rightarrow 3, Q \rightarrow 4, R \rightarrow 2, S \rightarrow 5$

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