A) \[{{v}_{f}}^{2}={{v}_{i}}^{2}+\frac{2GM}{{{M}_{e}}R}\left( 1-\frac{1}{10} \right)\]
B) \[{{v}_{f}}^{2}={{v}_{i}}^{2}+\frac{2G{{M}_{e}}}{{{\operatorname{R}}_{e}}}\left( 1+\frac{1}{10} \right)\]
C) \[{{v}_{f}}^{2}={{v}_{i}}^{2}+\frac{2G{{M}_{e}}}{{{\operatorname{R}}_{e}}}\left( 1-\frac{1}{10} \right)\]
D) \[{{v}_{f}}^{2}={{v}_{i}}^{2}+\frac{2GM}{{{\operatorname{R}}_{e}}}\left( 1-\frac{1}{10} \right)\]
Correct Answer: C
Solution :
[c] \[-\frac{G{{M}_{e}}m}{10{{\operatorname{R}}_{e}}}+\frac{1}{2}m{{v}_{i}}^{2}=-\frac{G{{M}_{e}}m}{{{\operatorname{R}}_{e}}}+\frac{1}{2}m{{v}_{f}}^{2}\] \[\therefore {{v}_{f}}^{2}={{v}_{i}}^{2}+\frac{2G{{M}_{e}}}{{{\operatorname{R}}_{e}}}\left( 1-\frac{1}{10} \right)\].You need to login to perform this action.
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