The expression for the acceleration due to gravity $g$ on the surface of the Earth in terms of its mass $M$ and radius $R$ is:

1. Gravitational force on a body: $F = \dfrac{GMm}{r^2}$. 2. By Newton's second law this force gives weight $F = mg$. 3. Equating, $mg = \dfrac{GMm}{r^2}$, so $g = \dfrac{GM}{r^2}$. 4. On the surface $r = R$, hence $g = \dfrac{GM}{R^2}$; the radius appears squared. _Source: Balbharati (Maharashtra Board) Class 10 Science & Technology, Ch 1 "Gravitation", p.17_