A) 4 R
B) \[\frac{R}{4}\]
C) 2 R
D) \[\frac{R}{2}\]
Correct Answer: B
Solution :
The acceleration due to gravity \[g=\frac{GM}{{{R}^{2}}}\] At a height h above the earth?s surface, the acceleration due to gravity is \[g'=\frac{GM}{{{(R+h)}^{2}}}\] \[\therefore \] \[\frac{g}{g'}={{\left( \frac{R+h}{R} \right)}^{2}}={{\left( 1+\frac{h}{R} \right)}^{2}}\] \[\frac{g}{g'}={{\left( 1+\frac{h}{R} \right)}^{-2}}\] \[=\left( 1-\frac{2\,h}{R} \right)\] but \[g'=\frac{g}{2}\] (given) \[\therefore \] \[\frac{g/2}{g}=1-\frac{2\,h}{R}\] \[\frac{2h}{R}=\frac{1}{2}\] \[h=\frac{R}{4}\]
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