A) \[\frac{{{R}_{1}}}{{{R}_{2}}}\]
B) \[{{\left( \frac{{{R}_{1}}}{{{R}_{2}}} \right)}^{2}}\]
C) \[\frac{{{R}_{2}}}{{{R}_{1}}}\]
D) \[{{\left( \frac{{{R}_{2}}}{{{R}_{1}}} \right)}^{2}}\]
E) \[{{\left( \frac{{{R}_{1}}}{{{R}_{2}}} \right)}^{1/2}}\]
Correct Answer: B
Solution :
Radius of circular path \[R=\frac{mv}{qB}\] but \[mv=\sqrt{2mqV}\] \[\therefore \] \[R=\frac{\sqrt{2mqV}}{qB}\]or \[R\propto \sqrt{m}\] Or \[\frac{R_{1}^{2}}{R_{2}^{2}}=\frac{{{M}_{1}}}{{{M}_{2}}}\]or \[\frac{{{M}_{1}}}{{{M}_{2}}}=\frac{R_{1}^{2}}{R_{2}^{2}}={{\left( \frac{{{R}_{1}}}{{{R}_{2}}} \right)}^{2}}\]
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