A) \[\frac{{{v}_{1}}}{{{v}_{2}}}=\frac{{{m}_{1}}}{{{m}_{2}}}\]
B) \[\frac{{{v}_{2}}}{{{v}_{1}}}=\frac{{{m}_{1}}}{{{m}_{2}}}\]
C) \[\frac{{{v}_{1}}}{{{v}_{2}}}={{\left( \frac{{{m}_{1}}}{{{m}_{2}}} \right)}^{2}}\]
D) \[\frac{{{v}_{1}}}{{{v}_{2}}}=\sqrt{\frac{{{m}_{1}}}{{{m}_{2}}}}\]
Correct Answer: D
Solution :
The escape velocity on a planet is given by \[{{v}_{es}}=\sqrt{\frac{GM}{R}}\Rightarrow {{v}_{es}}\propto \sqrt{m}\] (since, radius is same) Hence, \[\frac{{{v}_{1}}}{{{v}_{2}}}=\sqrt{\frac{{{m}_{1}}}{{{m}_{2}}}}\]
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