A) \[3R\]
B) \[\sqrt{2}R\]
C) \[(\sqrt{2}-1)R\]
D) \[\frac{1}{\sqrt{2}}R\]
Correct Answer: C
Solution :
The value of acceleration due to gravity at height h (when h is not negligible as compared to R) \[g=g\frac{{{R}^{2}}}{{{(R+h)}^{2}}}\] Here, \[g=\frac{g}{2}\] \[\therefore \] \[\frac{g}{2}=g\frac{{{R}^{2}}}{{{(R+h)}^{2}}}\] or \[\frac{1}{2}=\frac{{{R}^{2}}}{{{(R+h)}^{2}}}\] or \[\sqrt{\frac{1}{2}}=\frac{R}{R+h}\] or \[R+h=\sqrt{2}R\] \[\therefore \] \[h=(\sqrt{2}-1)R\]
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