Question

Suppose that a drill is able to reach a depth below the Earth s surface equal to 10% of the radius of the Earth (i.e., a distance from the center of the Earth equal to 90% of the radius). What is the acceleration due to gravity at the bottom of this shaft?

Answer 1

Acceleration due to gravity at Earth surface = GM/R²

                                                                                                        = G * (density * 4/3 pi R)

Acceleration due to gravity at distance r from Earth centre =   GM'/r²

                                                                                              = G * (density * 4/3 pi r³)/r²

                                                                                                                                        =   G * (density * 4/3 pi r)

=>   acceleration due to gravity at the bottom of this shaft =   (9.8/R) * r

                                                                                             =    (9.8/R) * 0.9R

                                                                                          =   8.82 m/sec²