A2 Daily A Level Physics question
Which statement must be true when testing whether the gravitational field strength g around a spherical planet follows a 1/r² model? A probe finds g = 6.0 N kg^-1 at r = 2000 km from the planet’s centre. At r = 4000 km, which reading would best support the 1/r² model?
Answer
The correct answer is D.
Correct: D — 1.5 N kg^-1. For a 1/r² dependence, doubling r reduces g by a factor of 4: g₂ = 6.0 × (2000/4000)² = 6.0 × (1/2)² = 1.5 N kg^-1. A halves g (1/r), which is the wrong proportionality. B suggests no change with distance, contradicting any inverse dependence. C applies a 1/r³ model, giving 6.0/8 = 0.75 N kg^-1, which is too small. D correctly applies the inverse-square check for a doubled distance.