A) \[2\]
B) \[\frac{1}{2}\]
C) \[\frac{1}{\sqrt{2}}\]
D) \[\sqrt{2}\]
Correct Answer: B
Solution :
Key Idea: Kinetic energy of satellite is half of its potential energy. Potential energy of satellite \[U=-\frac{G{{M}_{e}}m}{{{R}_{e}}}\] where \[{{R}_{e}}\] is radius of earth, \[{{M}_{e}}\] the mass of earth, \[m\] the mass of satellite and \[G\] the gravitational constant. \[|U|\,\,=\frac{G{{M}_{e}}m}{{{R}_{e}}}\] Kinetic energy of satellite \[K=\frac{1}{2}\frac{G{{M}_{e}}m}{{{R}_{e}}}\] Thus \[\frac{K}{|U|}=\frac{1}{2}\frac{G{{M}_{e}}m}{{{R}_{e}}}\frac{{{R}_{e}}}{G{{M}_{e}}m}\] \[=\frac{1}{2}\]
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