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BCECE Engineering BCECE Engineering Solved Paper-2009

  • question_answer
    An \[\alpha -\]particle and a deuteron projected with equal kinetic energies describe circular paths or radii \[{{r}_{1}}\] and\[{{r}_{2}}\] respectively in a uniform magnetic field. The ratio\[{{\text{r}}_{\text{1}}}\text{/}{{\text{r}}_{\text{2}}}\] is

    A)  1                                            

    B)  2

    C)  \[\frac{1}{\sqrt{2}}\]                    

    D)         \[\sqrt{2}\]

    Correct Answer: D

    Solution :

    Given, \[{{K}_{\alpha }}={{K}_{d}}=K,{{q}_{\alpha }}=q={{q}_{d}},{{m}_{\alpha }}=2{{m}_{d}}\] For\[\alpha -\]particle\[{{r}_{1}}=\frac{\sqrt{2{{m}_{1}}K}}{Bq}\] For deuteron \[{{r}_{2}}=\frac{\sqrt{2{{m}_{2}}K}}{Bq}\] \[\therefore \]  \[\frac{{{r}_{1}}}{{{r}_{2}}}=\sqrt{2}\]\[\left( \because \,{{m}_{2}}=\frac{{{m}_{1}}}{2} \right)\]


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