Gravitational field strength g
● VERBATIM — examined word-for-wordGravitational field strength at a point is the gravitational force per unit mass exerted on a small test mass placed at that point. Vector, unit N kg⁻¹.
g = F/m, and for a point mass g = GM/r²What this actually means
Word for word, this is force per unit MASS. The single most common one-mark loss in the whole topic is writing 'the force acting on a mass at that point', which is just force, not force per unit mass. The words 'per unit mass' must physically appear.
Say small test mass, not just mass. A large test mass has its own gravitational field, which would pull the source around and distort the very field you are trying to measure. Small keeps that disturbance negligible. That is a separate mark in a two-mark version of this question.
g is a vector. It points towards the mass creating it, always, because gravity is only ever attractive. When two bodies are involved you must add the two g values by direction, and they can cancel to exactly zero at a neutral point.
Units: N kg⁻¹. If a synoptic units MCQ turns up, derive it from g = F/m rather than guessing. And note N kg⁻¹ is dimensionally identical to m s⁻², which is exactly why g doubles as the acceleration of free fall.
Two formulae live under this one heading and they are not the same statement. g = F/m is the definition, true everywhere and for any source. g = GM/r² is the result for a point mass (or outside a uniform sphere). Quote the definition when asked to define, the point-mass form when asked to calculate.
Writing 'the force on a mass' instead of 'the force per unit mass', and forgetting the word 'small'.
Prove it — watch it be true
- Pick the Earth planet preset and place the test mass probe at some radius.
- Read off the F readout and the g readout together and check F/g equals the probe mass you set.
- Change the probe mass and confirm F changes but g does not, because g is per unit mass.