A) \[{{\left( 1+\frac{h}{R} \right)}^{2}}\]
B) \[{{\left( 1+\frac{R}{h} \right)}^{2}}\]
C) \[{{\left( \frac{R}{h} \right)}^{2}}\]
D) \[{{\left( \frac{h}{R} \right)}^{2}}\]
Correct Answer: A
Solution :
The value of acceleration due to gravity g at a height h above the surface of earth is \[{{g}_{h}}=\frac{g}{{{\left( 1+\frac{h}{R} \right)}^{2}}}\] where R is radius of earth. \[\therefore \] \[\frac{g}{{{g}_{h}}}={{\left( 1+\frac{h}{R} \right)}^{2}}\] Note: If the height is negligible compared to radius of earth, then \[{{g}_{h}}=g{{\left( 1+\frac{h}{R} \right)}^{2}}=g\left( 1-\frac{2h}{g} \right)\] Also, g decreases on going below the surface of the earth.
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