A) 64 km below the surface of the Earth
B) 64 km above the surface of the Earth
C) 30 km above the surface of the Earth
D) 32 km below the surface of the Earth.
Correct Answer: A
Solution :
Let g be the acceleration due to gravity at the surface of the Earth. At a certain place, acceleration due to gravity becomes, \[g'=g-1%\] of \[g=g-\frac{g}{100}=0.99g\] At height h, acceleration due to gravity becomes, \[g'=g\left( 1-\frac{2h}{R} \right)\Rightarrow 0.99g=g\left( 1-\frac{2h}{R} \right)\] \[0.99=1-\frac{2h}{R};\frac{2h}{R}=1-0.99=0.01\] \[h=\frac{0.01\times R}{2}=\frac{0.01\times 6400}{2}km=32km\] At depth d, acceleration due to gravity is given by \[g'=g\left( 1-\frac{d}{R} \right)\Rightarrow 0.99g=g\left( 1-\frac{d}{R} \right)\] \[\frac{d}{R}=1-0.99=0.01\] \[d=0.01\times R=0.01\times 6400km=64km\]
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