KVPY Sample Paper KVPY Stream-SX Model Paper-22

  • question_answer
    A thin uniform ring of radius \[R\] carrying uniform charge \[Q\] and mass \[M\] rotates about its axis with angular velocity \[\omega \]. The ratio of its magnetic moment and angular momentum is:

    A) \[\frac{Q}{M}\]

    B) \[\frac{M}{Q}\]

    C) \[\frac{Q}{2M}\]           

    D) \[\frac{M}{2Q}\]

    Correct Answer: C

    Solution :

    \[M=iA=\frac{Q}{T}A=\frac{Q\omega }{2\pi }\times \pi {{R}^{2}}=\frac{Q\omega {{R}^{2}}}{2}\]
    \[L=I\omega =M{{R}^{2}}\omega \]
    \[\therefore \]      \[\frac{M}{L}=\frac{Q\omega {{R}^{2}}/2}{M{{R}^{2}}\omega }=\frac{Q}{2M}.\]

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