KVPY Sample Paper KVPY Stream-SX Model Paper-5

  • question_answer
    Two particles having the same specific charge (q/m) enter a uniform magnetic field with the same speed but an angles of \[30{}^\circ \] and \[60{}^\circ \] with the field. Let a, b and c be ratios of their pitches, radii and periods of their paths respectively, then-

    A) \[a+b=2\sqrt{c}\]         

    B) \[abc=1\]

    C) \[{{a}^{2}}=c\]                      

    D) \[a{{b}^{2}}=c\]

    Correct Answer: A

    Solution :

    [B] \[T=\frac{2\pi m}{qB},\] \[p=\frac{2\pi m}{qB}v\cos \theta ,\] \[R=\frac{mv\sin \theta }{qB}\] \[a=\frac{\cos {{\theta }_{1}}}{\cos {{\theta }_{2}}},\] \[b=\frac{\sin {{\theta }_{1}}}{\sin {{\theta }_{2}}},\]\[c=1\] \[a=\sqrt{3},\] \[b=\frac{1}{\sqrt{3}},\] \[c=1.\]  

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