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MGIMS WARDHA MGIMS WARDHA Solved Paper-2014

  • question_answer
    Two particles A and B of masses m and 2m have charges\[q\]and\[2q\]respectively. Both particles moving with velocities\[{{\upsilon }_{1}}\]and\[{{\upsilon }_{2}}\] respectively in the same direction and   enter the same magnetic field B acting normally to their direction of motion. If the two forces\[{{F}_{A}}\]and\[{{F}_{B}}\]acting on them are in the ratio of\[1:2,\] the ratio of their velocities is

    A)  \[2:1\]                                 

    B)  \[3:2\]

    C)  \[2:3\]                                 

    D)  \[1:1\]

    Correct Answer: D

    Solution :

                     The magnetic Lorentz force acts on charge particle given by \[F=qvB\text{ }sin\theta \] \[\frac{{{F}_{A}}}{{{F}_{B}}}=\frac{{{q}_{1}}{{v}_{1}}B\sin 90{}^\circ }{{{q}_{2}}{{v}_{2}}B\sin 90{}^\circ }\] Or           \[1/2=(q/2q)({{v}_{1}}/{{v}_{2}})\] \[\therefore \]  \[\frac{{{v}_{1}}}{{{v}_{2}}}=1/1\]


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