Question

At what distance from the surface of the earth ,the value of 'g' becomes 9% of its value on the surface?(Re=6400km)

Answer 1

The distance from the surface of the earth ,the value of 'g' becomes 9% of its value on the surface is ≈ 21333.3 Km

• We know the formula for the value of g at point P is :

                                  g = GM/R²

• Where G = Gravitational constant
• R =  Distance from earth's center to the point
• M = Mass of earth
• Now say the distance to the surface is R1 and gravitational acc. g
• The distance to the point P required in our question is R2 and acc. g1.
• So, taking ratio of g and g1 we get,

                     g1/g = (R/R1)²

• Now we know g1/g = 0.09
• Hence, R/R1 = √(g1/g) = 0.03
• R1 = R/.03 = 6400/.03 Km ≈ 21333.3 Km