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一、原题展示2011年全国高考新课程卷第21题;假设地球是一半径为R、质量均匀分布的球体.一矿井深度为d.已知质量分布均匀的球壳对壳内物体的引力为零.矿井底部和地面处的重力加速度大小之比为()A.1-d/R B.1+d/RC.((R-d)/R)~2 D.(R/(R-d))~2二、问题解析设地球的质量为M,地球表面处的重力加速度为g,矿井底部的重力加速度为g′.若不计地球的自转,在地球表面,对质量为m的物体,由万有引力定律,有mg=G(Mm)/(R~2)设地球的密度为ρ,则M=4/5πR~3ρ位于矿井深度为d处的物体,地球对它的作用可
First, the original title shows the 2011 National College Entrance Examination curricula 21 questions; assume that the Earth is a radius R, uniform mass distribution of the sphere. Mine a depth of d. Known mass distribution of spherical shell on the object of gravity Is 0. The ratio of the gravitational acceleration at the bottom of the mine to the ground is () A.1-d / R B.1 + d / RC ((R d) / R) ~ 2 D. (R / (Rd)) ~ 2 Second, the problem is solved Set the mass of the Earth M, the Earth’s surface gravity acceleration of g, the bottom of the mine gravity acceleration g ’. If you do not consider the Earth’s rotation, the Earth’s surface, the mass of m objects by gravitation The law, with mg = G (Mm) / (R ~ 2) Let the density of the Earth be ρ, then M = 4 / 5πR ~ 3ρ is located in the depth of the mine d at the object, the Earth on its role