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KVPY Sample Paper KVPY Stream-SX Model Paper-4

  • question_answer
    A conducting rod of mass in and \[\ell \] is placed on a smooth horizontal surface in a region where transverse uniform magnetic field B exists in the region.\[\operatorname{At}\,t= 0\], constant force F starts acting on the rod at its mid-point as shown. Potential difference between ends of the rod, \[{{V}_{P}}-\text{ }{{\text{V}}_{Q}}\]at any time \[t\] is

    A) \[\frac{BF\ell t}{2m}\]               

    B) \[\frac{BF\ell t}{4m}\]

    C) \[\frac{5BF\ell t}{8m}\]              

    D) \[\frac{7BF\ell t}{8m}\]

    Correct Answer: A

    Solution :

    [a]
    velocity at any time \[t,\]
    \[v=a\,t=\frac{F}{m}t\]
    Now, \[e={{V}_{P}}-{{V}_{Q}}=Bv\ell \sin 30{}^\circ \]
    \[=B\left( \frac{Ft}{m} \right)\ell \times \frac{1}{2}=\frac{BF\ell t}{2m}\]


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