A) \[1:1:1\]
B) \[1:\sqrt{2}:\sqrt{2}\]
C) \[\sqrt{2}:1:1\]
D) \[\sqrt{2}:\sqrt{2}:1\]
E) \[1:\sqrt{2}:1\]
Correct Answer: B
Solution :
Radius of circular paths is proportional to square root of mass. \[R\propto \sqrt{m}\] \[\frac{{{R}_{d}}}{{{R}_{p}}}=\sqrt{\frac{{{m}_{d}}}{{{m}_{p}}}}=\frac{\sqrt{2}}{1}\] \[\Rightarrow \] \[\frac{{{R}_{p}}}{{{R}_{d}}}=\frac{1}{\sqrt{2}}\] Also, \[\frac{{{R}_{d}}}{{{R}_{\alpha }}}=\frac{\sqrt{{{M}_{d}}}}{\sqrt{{{M}_{\alpha }}}}=\frac{\sqrt{2}}{\sqrt{4}}=\frac{1}{\sqrt{2}}\] Hence, ratio is\[1:\sqrt{2}:\sqrt{2}.\]
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