What is meant by acceleration due to gravity? Derive g = GM/R² and explain why g is not the same everywhere on the earth.

1. 1 · Define. g is the acceleration produced in a freely falling body by the earth's gravitational pull.
2. 2 · Equate the two forces. Second law: F = mg. Law of gravitation: F = GMm/R².
3. 3 · Derive. mg = GMm/R², so g = GM/R². The mass m cancels, so g is the same for all bodies at a place.
4. 4 · Explain the change. The earth is flattened at the poles, so R is smaller there and g is larger. g is least at the equator.
5. 5 · Close. The average value used near the surface is 9.8 m s⁻².

Scoring tip: Write both force equations before you equate them. Say clearly that m cancels, so g does not depend on mass.