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 \[g={{\left( 1+\frac{h}{R} \right)}^{2}}=g\,\left( 1-\frac{2\,h}{R} \right)\] Given, \[g=\frac{g}{4}\] \[\frac{g}{4}=g\,\left( 1-\frac{2h}{R} \right)\] \[\Rightarrow \] \[\frac{1}{4}=1-\frac{2\,h}{R}\] \[\Rightarrow \] \[h=\frac{3\,R}{8}\] 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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