How is the acceleration due to gravity on the surface of the earth related to it's mass and radius ?

The value of 'g' on earth depends on the value of mass and radius of earth.

Let, g be the acceleration due to gravity of earth of mass M and radius R.

By newton's law of motion, the force due to gravity on a body of mass m on it's surface will be

F = mass x acceleration due to gravity

or F = mg     [Equation 1]

By Newton's gravitational law, this attractive force is given by

F = $\text{G}\dfrac{\text{M}\text{m}}{\text{R}^2}$     [Equation 2]

From eqn. 1 and 2 we get,

$\text{G}\dfrac{\text{M}\text{m}}{\text{R}^2} = \text{m}\text{g}$

⇒ acceleration due to gravity g = $\dfrac{\text{G}\text{M}}{\text{R}^2}$.