This question is about gravitational field strength near the surface of a planet: State why gravitational field strength at a point is numerically equal to the acceleration of free fall at that point
Gravitational field strength at a point is numerically equal to the acceleration of free fall at that point because both quantities measure the same physical phenomenon: the force experienced by a mass due to gravity.
Gravitational field strength, denoted by g, is a measure of the force per unit mass that a mass experiences in a gravitational field. It is defined as the force experienced by a unit mass placed at that point. Therefore, the numerical value of g represents the force per unit mass, or acceleration, experienced by an object in free fall at that point.
Acceleration of free fall, denoted by g as well, represents the acceleration experienced by an object in free fall due to the force of gravity. It is the acceleration with which an object falls under the influence of gravity, neglecting any other external forces.
Since both gravitational field strength and acceleration of free fall represent the same force experienced by a mass due to gravity, they have the same numerical value at a given point. This is a fundamental principle in understanding the relationship between gravity and acceleration on a planet's surface.