A) \[-\,mg{{R}_{e}}\]
B) \[-0.67\,mg{{R}_{e}}\]
C) \[-0.5\,mg{{R}_{e}}\]
D) \[-0.33\,mg{{R}_{e}}\]
Correct Answer: C
Solution :
Gravitational potential energy of a satellite at height h \[U=\frac{G{{M}_{e}}m}{{{R}_{e}}+h}\] ?(1) Here \[h=R{{ & }_{e}}=\]radius of earth and \[g=\frac{G{{M}_{e}}}{R\,_{e}^{2}}\] \[\Rightarrow \] \[G{{M}_{e}}=R_{e}^{2}g\] ...(2) \[\therefore \] \[U=\frac{(R_{e}^{2}g)m}{{{R}_{e}}+{{R}_{e}}}=-\frac{1}{2}mg{{R}_{e}}\] \[=-5.0\,mg\,{{R}_{e}}\]
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