At what distance above the surface of the earth is the acceleration due to the earth’s gravity 0.980 m/s2 if the acceleration due to gravity at the surface has magnitude 9.80 m/s2?

Problem 11E Solution 11 E Step 1 : Introduction : In this question, we need to find at what distance above the earth will the gravitational force will have 2 magnitude 0.980 m/s Data given 2 Gravitational force on earth G =e9.8 m/s Gravitational force from surface of earth G = 0.98 m/s 2 x This can be solved using Inverse square law 2 G e G 2xx Substituting values we get 9.8 m/s = 0.98 m/s × 2 × x 2 2 x = 4.68 x = 2.163 m Since we are measuring from the surface of the earth we shall consider the radius of the earth We have 6 R e 6.37 × 10 m Hence we get the distance as 6 x = 2.163 m × 6.37 × 10 m x = 1.378 × 10 m8 8 This can be approximated to x = 1.38 × 10 m Hence the gravitational force will be 0.98 m/s at the distance 1.38 × 10 m from the surface of the earth