A) \[3.2\times {{10}^{3}}\text{ }km\]
B) \[1.6\times {{10}^{3}}km\]
C) \[1.28\times {{10}^{4}}km\]
D) \[6.4\times {{10}^{3}}km\]
Correct Answer: A
Solution :
\[{{E}_{2}}\,=\,\frac{GMm}{2(R+h)}\] \[{{E}_{1}}\,=\,\frac{GMm}{R}\,-\,\frac{GMm}{(R+h)}\] \[\,\frac{GMm}{2(R+h)}\,=\,GMm\,\left[ \frac{1}{R}-\frac{1}{R+h} \right]\] \[\frac{1}{2(R+h)}\,\,=\,\left[ \frac{R+h-R}{R(R+h)} \right]\] \[h=\frac{R}{2}\,=\,\frac{6.4\,\times \,{{10}^{3}}}{2}\,\,=\,\,3.2\,\times \,{{10}^{3}}\,km\]
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