A) \[-2\,mg{{R}_{e}}\]
B) \[2\,mg{{R}_{e}}\]
C) \[\frac{1}{2}mg{{R}_{e}}\]
D) \[-\frac{1}{2}mg{{R}_{e}}\]
Correct Answer: D
Solution :
\[\Delta U={{U}_{2}}-{{U}_{1}}=\frac{mgh}{1+\frac{h}{{{R}_{e}}}}=\frac{mg{{R}_{e}}}{1+\frac{{{R}_{e}}}{{{R}_{e}}}}=\frac{mg{{R}_{e}}}{2}\] \[\,\Rightarrow \,{{U}_{2}}-(-mg{{R}_{e}})=\frac{mg{{R}_{e}}}{2}\]Þ \[{{U}_{2}}=-\frac{1}{2}mg{{R}_{e}}\]
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