A) \[\left( {{R}_{1}}/{{R}_{2}} \right)\]
B) \[\left( {{R}_{2}}/{{R}_{1}} \right)\]
C) \[{{\left( {{R}_{1}}/{{R}_{2}} \right)}^{2}}\]
D) \[\left( {{R}_{1}}/{{R}_{2}} \right)\]
Correct Answer: C
Solution :
\[\frac{1}{2}m{{v}^{2}}=qV\] or \[v=\sqrt{\frac{2qV}{m}}\] Centripetal force \[\frac{m{{v}^{2}}}{R}=q\times B\times v\] \[\therefore \] \[v=\frac{qBR}{m}\] Hence, \[\sqrt{\frac{2qV}{m}}=\frac{qBR}{m}\] or \[R={{\left( \frac{2mV}{q} \right)}^{1/2}}\times \frac{1}{B}\] Here, V, q and B are constants, Hence, \[R\,\,\alpha \,\,m\] So, \[\frac{{{m}_{1}}}{{{m}_{2}}}={{\left( \frac{{{R}_{1}}}{{{R}_{2}}} \right)}^{2}}\]
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