A) \[{{\left( \frac{{{R}_{1}}}{{{R}_{2}}} \right)}^{2}}\]
B) \[\left( \frac{{{R}_{1}}}{{{R}_{2}}} \right)\]
C) \[{{\left( \frac{{{R}_{1}}}{{{R}_{2}}} \right)}^{\frac{1}{2}}}\]
D) \[\frac{{{R}_{2}}}{{{R}_{1}}}\]
Correct Answer: A
Solution :
\[R=\frac{mv}{qB}=\sqrt{\frac{2m{{E}_{K}}}{qB}}=\sqrt{\frac{2mqv}{qB}}\] \[i.e.\] \[R\propto \sqrt{m}\]or \[m\propto {{R}^{2}}\] \[\therefore \]Ratio of \[X\] to that of\[Y\], \[\frac{{{m}_{1}}}{{{m}_{2}}}\propto {{\left( \frac{{{R}_{1}}}{{{R}_{2}}} \right)}^{2}}\]
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