A) 2660.0 km
B) 2689.0 km
C) 2559.6 km
D) 2649.6 km
Correct Answer: D
Solution :
Let g be acceleration due to gravity on earth and g? be acceleration due to gravity at height h Then, \[\frac{g'}{g}={{\left( \frac{R}{R+H} \right)}^{2}}\] Given, \[\frac{g'}{g}=\frac{1}{2}\] \[\frac{1}{2}={{\left( \frac{R}{R+H} \right)}^{2}}\] \[\frac{R}{R+H}=\frac{1}{\sqrt{2}}\,\,\,\Rightarrow \,\,\frac{h}{R}\,=\sqrt{2}-1=0.414\] So, \[h\,\,=\, 0.414 \times \,\,R\] \[=\,\,\,0.414\,\,\times \,\,6400 km\] \[\operatorname{V}\,\,=\, 2649.6 km\]
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