AIIMS AIIMS Solved Paper-2015

  • question_answer
    A wire having mass m and length 1 can freely slide on a pair of parallel smooth horizontal rails placed in vertical magnetic field B. The rails are connected by a capacitor of capacitance C. The electric resistance of the rails and the wire is zero. If a constant force F acts on the wire as shown in the figure. Then, the acceleration of the wire can be given as

    A) \[\left( \text{kJ mo}{{\text{l}}^{\text{-1}}} \right)\]        

    B) \[\left( \text{kJ mo}{{\text{l}}^{\text{-1}}} \right)\]

    C) \[{{\left[ \text{Co}{{\left( \text{N}{{\text{H}}_{\text{3}}} \right)}_{\text{4}}}\text{C}{{\text{l}}_{\text{2}}} \right]}^{+}}\]                  

    D) \[\text{I}\]

    Correct Answer: D

    Solution :

    Let the velocity of wire is v at time t and the emf induced is\[{{R}_{1}}\], then charge (in magnitude) appeared on the plates of capacitor is \[{{R}_{2}}\] Now current, \[\frac{{{R}_{1}}}{{{R}_{2}}}\]\[\left| \frac{dL}{dt} \right|\] The force due to the current is \[2\,\,m\,\,{{l}^{3}}{{\omega }^{2}}\sin \theta .\cos \theta \] So, net force in the direction of motion of conductor wire \[\,m\,\,{{l}^{2}}{{\omega }^{2}}\sin 2\theta \] \[\,m\,\,{{l}^{2}}\sin 2\theta \]


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