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