A) \[\frac{1}{R}\]
B) \[\frac{1}{\sqrt{R}}\]
C) \[R\]
D) \[\frac{1}{{{R}^{3}}}\]
Correct Answer: A
Solution :
\[\frac{G{{M}_{e}}m}{{{R}^{2}}}=\frac{mv_{0}^{2}}{R}\] \[v_{0}^{2}=\sqrt{\frac{G{{M}_{e}}}{R}},KE=\frac{1}{2}mv_{0}^{2}\] \[KE=\frac{1}{2}m{{\left( \frac{G{{M}_{e}}}{R} \right)}^{2/2}}=\frac{1}{2}\frac{mG{{M}_{e}}}{R}\] \[v\propto \frac{1}{R}\]
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