A) 3.10 m/s
B) \[5.06\,m/{{s}^{2}}\]
C) \[7.64\,m/{{s}^{2}}\]
D) \[9.66\,m/{{s}^{2}}\]
Correct Answer: D
Solution :
Here: Depth \[=100\,km=100\times {{10}^{3}}m\] Radius of earth \[R=6380\,\times {{10}^{3}}\,m\]. Acceleration due to gravity below the earths surface is given by \[g=g\left( 1-\frac{d}{R} \right)\] \[g=9.8\left[ 1-\frac{100\times {{10}^{3}}}{6380\times {{10}^{3}}} \right]\] \[=9.8\left[ 1-\frac{1}{63.8} \right]\] \[=9.8\times \frac{62.8}{63.8}=9.66\,m/{{s}^{2}}\]
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