A) \[\frac{1}{R}\]
B) \[\frac{1}{\sqrt{R}}\]
C) \[R\]
D) \[\frac{1}{{{R}^{3/2}}}\]
Correct Answer: A
Solution :
Key Idea: Gravitational force provides the required centripetal force. The gravitational force provides the required centripetal force in orbit of earth. \[\therefore \] \[\frac{G{{M}_{e}}m}{{{R}^{2}}}=\frac{m{{v}_{e}}^{2}}{R}\] \[\Rightarrow \] \[{{v}_{0}}=\sqrt{\frac{G{{M}_{e}}}{R}}\] Kinetic energy \[=\frac{1}{2}m\,{{v}_{0}}^{2}\] \[\therefore \] \[KE=\frac{1}{2}m{{\left( \frac{G{{M}_{e}}}{R} \right)}^{2/2}}=\frac{1}{2}\frac{mG{{M}_{e}}}{R}\] \[\Rightarrow \] \[KE\propto \frac{1}{R}.\]You need to login to perform this action.
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