Question

show show that if a body is taken by height above the Earth's surface acceleration due to the gravity is decreases by the factor of radius square by (R+H )² where is R is the radius of the earth
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Answer 1

we know that acceleration due to gravity of earth is

g = GM/ R^2

now at height H above surface of earth acceleration due to gravity must be

g' = GM/(R+H)^2

now divide both

g'/g = R^2/(R+H)^ 2

g' = g(R)^2 / (R+H)^2