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