A) \[{{\left( \frac{2{{R}_{1}}}{{{R}_{2}}} \right)}^{2}}\]
B) \[{{\left( \frac{{{R}_{1}}}{2{{R}_{2}}} \right)}^{2}}\]
C) \[\frac{R_{1}^{2}}{2R_{2}^{2}}\]
D) \[\frac{2{{R}_{1}}}{{{R}_{2}}}\]
Correct Answer: C
Solution :
\[r=\frac{1}{B}\sqrt{\frac{2mV}{q}}\Rightarrow r\propto \sqrt{\frac{m}{q}}\Rightarrow \frac{{{r}_{x}}}{{{r}_{y}}}\times \sqrt{\frac{{{m}_{x}}}{{{q}_{x}}}\times \frac{{{q}_{y}}}{{{m}_{y}}}}\] \[\Rightarrow \frac{{{R}_{1}}}{{{R}_{2}}}=\sqrt{\frac{{{m}_{x}}}{{{m}_{y}}}\times \frac{2}{1}}\Rightarrow \frac{{{m}_{x}}}{{{m}_{y}}}=\frac{R_{1}^{2}}{2R_{2}^{2}}\]
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