A) \[v_{f}^{2}=v_{i}^{2}+\frac{2Gm}{{{M}_{e}}R}\left( 1-\frac{1}{10} \right)\]
B) \[v_{f}^{2}=v_{i}^{2}+\frac{2G{{M}_{e}}}{{{R}_{e}}}\left( 1+\frac{1}{10} \right)\]
C) \[v_{f}^{2}=v_{i}^{2}+\frac{2G{{M}_{e}}}{{{R}_{e}}}\left( 1-\frac{1}{10} \right)\]
D) \[v_{f}^{2}=v_{i}^{2}+\frac{2Gm}{{{R}_{e}}}\left( 1-\frac{1}{10} \right)\]
Correct Answer: C
Solution :
[c] \[-\frac{G{{M}_{e}}m}{10{{R}_{e}}}+\frac{1}{2}mv_{i}^{2}\]\[=-\frac{G{{M}_{e}}m}{{{\operatorname{R}}_{e}}}+\frac{1}{2}mv_{f}^{2}\] \[\therefore v_{f}^{2}=v_{i}^{2}+\frac{2G{{M}_{e}}}{{{\operatorname{R}}_{e}}}\left( 1-\frac{1}{10} \right)\]
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