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. Use words and equations
The gravitational field strength at a point is numerically equal to the acceleration of free fall at that point because both quantities are measurements of the force of gravity acting on an object.
The gravitational field strength, represented by the symbol g, is defined as the force per unit mass experienced by an object placed at that point in the gravitational field. Mathematically, it can be expressed as:
g = F/m,
where g is the gravitational field strength, F is the force of gravity acting on the object, and m is the mass of the object.
On the other hand, the acceleration of free fall, represented by the symbol g' or g with a subscript 'f', is the acceleration experienced by an object in free fall due to gravity. It can be calculated using Newton's second law of motion, which states that the force acting on an object is equal to the mass of the object multiplied by its acceleration. Mathematically, the equation can be written as:
F = mg',
where F is the force of gravity acting on the object, m is the mass of the object, and g' is the acceleration of free fall.
Since both the gravitational field strength and the acceleration of free fall describe the force of gravity acting on an object, it can be concluded that the numerical values of these two quantities are equal at any given point. Therefore, the gravitational field strength at a point is numerically equal to the acceleration of free fall at that point.