The correct relationship between "G" and "g" in a gravitational field is given by the equation (Where the symbols have their usual meanings)

Analyze the question: We need the relationship between G (the universal gravitational constant) and g (acceleration due to gravity) for a planet of mass M and radius R.

Concept: Newton's law of universal gravitation says the force between two masses is:

F = GMm / R²

where M is the mass of the Earth (or planet), m is the mass of the object, and R is the distance from the centre of the planet (its radius, for an object on the surface).

Also, the weight of an object is:

F = mg

Solution: Equate the two expressions for the force:

mg = GMm / R²

Cancel m from both sides:

g = GM / R²

Checking the other options:

• A: GM/R has the wrong units (it is a potential, in J/kg, not an acceleration).
• C and D: they use M², but the planet's mass appears only once, because the object's mass m cancels.
• Only B has the correct inverse-square dependence on R and the correct power of M.

Answer: Option B

Tip: Remember that g comes from "force per unit mass." Start with F = GMm/R², divide by m, and you get g = GM/R². Also note the inverse-square rule: gravity weakens with the square of the distance.