(c) gravitational field strength is uniform close to the surface of the…

The idea

Close to the Earth's surface, over distances small compared with the Earth's radius, the gravitational field strength g is effectively uniform: its magnitude and direction are the same everywhere in that region. Numerically g equals the acceleration of free fall, about 9.81 m s⁻², because a freely falling object experiences only the gravitational force, so Newton's second law gives a = F/m = g. The two quantities share the same value but differ in meaning: field strength is force per unit mass at a point, while acceleration of free fall is the acceleration of an object moving under gravity alone. Uniformity fails over large heights, where g decreases as 1/r².

What earns the marks

• States that near the Earth's surface the gravitational field is approximately uniform in magnitude and direction.
• Explains that g is numerically equal to the acceleration of free fall, approximately 9.81 m s⁻².
• Derives the equality from Newton's second law: for a freely falling body, mg = ma, so a = g.
• Distinguishes field strength (force per unit mass, N kg⁻¹) from acceleration (m s⁻²) while noting their numerical equivalence.
• Recognises that the uniform-field approximation breaks down at heights that are a significant fraction of the Earth's radius.

Common mistakes and how to put them right

• Claiming g and the acceleration of free fall are the same physical quantity.

  Put it right: They are numerically equal but conceptually distinct.

• Using g = 9.81 m s⁻² at all heights above the Earth.

  Put it right: The field weakens with distance and is only uniform close to the surface.

• Confusing the units N kg⁻¹ and m s⁻² as different in value.

  Put it right: They are equivalent units for the same numerical quantity.

• Forgetting that the uniform-field approximation requires the region to be small compared with the Earth's radius.

Exam tips

• Quote g as 9.81 m s⁻² unless the question specifies a different value such as 9.8 m s⁻².
• When asked to justify uniformity, refer to the small change in height compared with the Earth's radius.
• Show the link mg = ma explicitly when explaining why g equals the acceleration of free fall.
• Use N kg⁻¹ when discussing field strength and m s⁻² when discussing acceleration, even though the values match.