A) \[~~\frac{R}{8}~~~\]
B) \[~~\frac{3R}{8}~~~\]
C) \[~~\frac{3R}{4}~~~\]
D) \[\frac{R}{2}\]
Correct Answer: B
Solution :
The value of acceleration due to gravity at a height h above the surface of the earth is given by \[g=\frac{g}{{{\left( 1+\frac{h}{R} \right)}^{2}}}\] where R is radius of earth. When h is negligible compared to R, we have \[g=g{{\left( 1+\frac{h}{R} \right)}^{-2}}=g\left( 1-\frac{2h}{R} \right)\] Given. \[g=\frac{g}{4}\] \[\frac{g}{4}=g\left( 1-\frac{2h}{R} \right)\] \[\Rightarrow \] \[\frac{g}{4}=g\left( 1-\frac{2h}{R} \right)\] \[\Rightarrow \] \[\frac{1}{4}-1-\frac{2h}{R}\] \[\Rightarrow \] \[\frac{2h}{R}=\frac{3}{4}\] \[\Rightarrow \] \[h=\frac{3R}{8}\] Note: The value of acceleration due to gravity decreases on going above or below the surface of earth.You need to login to perform this action.
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