KVPY Sample Paper KVPY Stream-SX Model Paper-25

  • question_answer
    A metal rod of length  moving with an angular velocity  and velocity of its centre is v. Find potential difference between points A and B at the instant shown in figure. A uniform magnetic field of strength B exist perpendicular to plane of paper:

    A) \[B\,v\,\ell \]

    B) \[Bv\ell +\frac{1}{2}B\omega \,{{\ell }^{2}}\]

    C) \[B\omega \,\ell -\frac{1}{2}B\omega \,{{\ell }^{2}}\]

    D) \[Bv\,\ell +B\,\omega \,\,{{\left( \frac{\ell }{2} \right)}^{2}}\]

    Correct Answer: A

    Solution :

    Point P is at instantaneous rest,
    \[{{\varepsilon }_{1}}=\,\,|{{v}_{P}}-{{v}_{A}}|\,\,=\frac{1}{2}B\omega \,\,{{\left( \frac{\ell }{2}+\frac{v}{\omega } \right)}^{2}}\]
    \[{{\varepsilon }_{2}}=\,\,|{{v}_{P}}-{{v}_{B}}|\,\,=\frac{1}{2}B\omega \,\,{{\left( \frac{\ell }{2}-\frac{v}{\omega } \right)}^{2}}\]
    \[|{{v}_{A}}-{{v}_{B}}|\,\,={{\varepsilon }_{1}}-{{\varepsilon }_{2}}\]
    \[|{{v}_{A}}-{{v}_{B}}|\,\,=B\ell v\]

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