A) 3 R
B) \[\sqrt{2}\]R
C) \[\left( \sqrt{2}-1 \right)R\]
D) \[\frac{1}{\sqrt{2}}R\]
E) None of these
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, \[g=\frac{g}{2}\] \[\frac{g}{2}=g\frac{{{R}^{2}}}{{{(R+h)}^{2}}}\] or \[\frac{1}{2}=\frac{{{R}^{2}}}{{{(R+h)}^{2}}}\] or \[\sqrt{\frac{1}{2}}=\frac{R}{R+h}\] or \[R+h=\sqrt{2}R\] \[\therefore \] \[h=(\sqrt{2}-1)\,R\]
You need to login to perform this action.
You will be redirected in
3 sec
