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RAJASTHAN ­ PET Rajasthan PET Solved Paper-2006

  • question_answer
    Two particles X and Y hiving equal charges, after being accelerated through the same potential difference, enter a region of uniform magnetic field and describes circular path of radius \[{{R}_{1}}\] and \[{{R}_{2}}\] respectively. The ratio of mases of X to that of Y is

    A)  \[{{\left( \frac{{{R}_{1}}}{{{R}_{2}}} \right)}^{2}}\]

    B)  \[\frac{{{R}_{1}}}{{{R}_{2}}}\]

    C)  \[{{\left( \frac{{{R}_{1}}}{{{R}_{2}}} \right)}^{3}}\]

    D)  \[{{\left( \frac{{{R}_{1}}}{{{R}_{2}}} \right)}^{1/2}}\]

    Correct Answer: A

    Solution :

     \[{{E}_{k}}=\frac{{{q}^{2}}{{B}^{2}}{{R}^{2}}}{2m}\] The energies of particles are same, then \[m\propto {{R}^{2}}\] \[\therefore \] \[\frac{{{m}_{1}}}{{{m}_{2}}}={{\left( \frac{{{R}_{1}}}{{{R}_{2}}} \right)}^{2}}\]


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