At equal distances h above and below the surface of a uniform Earth, the acceleration due to gravity is the same. Find h in terms of Earth's radius R.
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Question

At equal distances h above and below the surface of a uniform Earth, the acceleration due to gravity is the same. Find h in terms of Earth's radius R.

G1 Physics · Accepted Answer

Step 1: At height h, gₐ/g=[R/(R+h)]². At depth h inside a uniform Earth, gᵦ/g=(R-h)/R=1-h/R. Step 2: Put x=h/R and equate: 1/(1+x)²=1-x. Step 3: For x≠0, 1-x-x²=0, so x=(√5-1)/2. Therefore h=[(√5-1)/2]R. In the source choices this corresponds to 'None', option D.