Answer: r*sqrt(M)/(sqrt(M)+sqrt(m)).
- A r*sqrt(M)/(sqrt(M)+sqrt(m))
- B r*M/(M+m)
- C r*sqrt(m)/(sqrt(M)+sqrt(m))
- D r/2
Correct answer: A. r*sqrt(M)/(sqrt(M)+sqrt(m))
Explanation: Field from M: GM/x<sup>2.</sup> Field from m: Gm/(r-x)<sup>2.</sup> Setting them equal gives x = r*sqrt(M)/(sqrt(M)+sqrt(m)), the distance from M.
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.