Answer: r.
- A 1/r<sup>2</sup>
- B 1/r
- C r
- D r<sup>2</sup>
Correct answer: C. r
Explanation: Only the mass within radius r acts, and that mass ∝ r<sup>3</sup>, so g = GM(r)/r<sup>2</sup> ∝ r<sup>3</sup>/r<sup>2</sup> = r. The field grows linearly with r inside.
g is maximum at Earth's surface; going up, it falls off as 1/r² (inverse-square); going down, it falls off linearly with depth (since only the mass enclosed within radius r contributes), reaching zero at the centre.
Concept context
Universal gravitation, orbital mechanics, gravitational potential, and escape velocity.