A) 1.25 km
B) 2.5 km
C) 5 km
D) 7.5 km
E) 10km
Correct Answer: E
Solution :
Acceleration due to gravity at the surface of earth \[{{g}_{h}}=g{{\left( 1+\frac{h}{R} \right)}^{-2}}\] \[{{g}_{h}}=g\left( g-\frac{2h}{R} \right)\] Acceleration due to gravity at depth d from the surface of the earth \[{{g}_{d}}=g\left( 1-\frac{d}{R} \right)\] Given: \[{{g}_{h}}={{g}_{d}}\] \[\therefore \] \[\frac{2h}{R}=\frac{d}{R}\] Or \[d=2h\] Or \[d=10\,km\]
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