A) \[-1/2M{{v}^{2}}\]
B) \[1/2M{{v}^{2}}\]
C) \[3/2M{{v}^{2}}\]
D) \[M{{v}^{2}}\]
Correct Answer: A
Solution :
Kinetic energy of the satellite \[=\frac{1}{2}M{{v}^{2}}\] Potential energy of the satellite \[(U)=-\frac{G{{M}_{e}}M}{{{R}_{e}}}\] But, \[G{{M}_{e}}=gR_{e}^{2}\] \[\therefore \] \[U=-\frac{gR_{e}^{2}M}{{{R}_{e}}}=-g{{R}_{e}}M\] Orbital velocity of a satellite \[v=\sqrt{g{{R}_{e}}}\] \[\therefore \] \[U=-M{{v}^{2}}\] \[\therefore \] Total energy of the satellite \[=\frac{1}{2}M{{v}^{2}}-M{{v}^{2}}\] \[=-\frac{1}{2}M{{v}^{2}}\]
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