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. \[\left| U \right|=\frac{G{{M}_{e}}m}{{{R}_{e}}}\] Kinetic energy of satellite \[K=\frac{1}{2}\frac{G{{M}_{e}}m}{{{R}_{e}}}\] Thus, \[\frac{K}{\left| U \right|}=\frac{1}{2}\frac{G{{M}_{e}}m}{{{R}_{e}}}\times \frac{{{R}_{e}}}{G{{M}_{e}}m}=\frac{1}{2}\]
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