A) \[\sqrt{{{R}_{1}}/{{R}_{2}}}\]
B) \[{{R}_{1}}/{{R}_{2}}\]
C) \[{{({{R}_{1}}/{{R}_{2}})}^{2}}\]
D) \[{{({{R}_{2}}/{{R}_{1}})}^{2}}\]
Correct Answer: C
Solution :
Radius of circular path followed by charged particle is given by \[R=\frac{mv}{qB}=\frac{\sqrt{2mK}}{qB}\] \[[\because \,p=mv=\sqrt{2mK}]\] where, \[K\]is kinetic energy of particle. Charged particle q is accelerated through some potential difference V, such that kinetic energy of particle is \[K=qV,\] \[\therefore \] \[R=\frac{\sqrt{2mqV}}{qB}\] As the two charged particles of same magnitude and being accelerated through same potential, enters into a uniform magnetic field region, then \[R\propto \sqrt{m}\] So, \[\frac{{{R}_{1}}}{{{R}_{2}}}=\sqrt{\frac{{{m}_{A}}}{{{m}_{B}}}}\Rightarrow \frac{{{m}_{A}}}{{{m}_{B}}}={{\left( \frac{{{R}_{1}}}{{{R}_{2}}} \right)}^{2}}\]
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