A simulation reports the pairs (distance r in arbitrary units, gravitational field g in arbitrary units) (1.0, 9.00), (1.5, 4.00), (2.0, 2.25), (2.5, 1.44), (3.0, 1.00). (a) Describe the pattern without calling it linear. [2] (b) Calculate gr² for every pair and use the values to test g ∝ 1/r². [4] (c) Predict g at r = 4.0 and explain the interpolation or extrapolation risk. [3] (d) State what this evidence can and cannot establish about real gravitational fields. [3]

Question

Accepted Answer

The field decreases non-linearly. Every gr² value is 9.00, so the dataset exactly follows g = 9/r²; at r = 4.0 the model predicts g = 0.5625. Simulation agreement does not independently verify nature. (a) As distance increases, field strength decreases by progressively smaller absolute amounts. A straight line through the raw g–r points would not describe the curved pattern. (b) The products gr² are 9.00×1.0² = 9.00, 4.00×1.5² = 9.00, 2.25×2.0² = 9.00, 1.44×2.5² = 9.00 and 1.00×3.0² = 9.00. (b) A constant gr² means g = constant/r² for these values, so the supplied record is exactly consistent with an inverse-square model. (c) At r = 4.0, g = 9.00/4.0² = 0.5625 arbitrary units. This is extrapolation beyond the measured 1.0–3.0 range and depends on the same model continuing to apply. (d) The evidence checks that the simulation implements an inverse-square rule over its sampled range. It does not measure a real source mass, establish the units, reveal uncertainty or independently test Newtonian gravity in nature.

Test an inverse-square gravitational field claim

What a complete response should do

Gravitational field against distance

Your self-assessment

Gravitational field against distance — supplied values
Distance / arbitrary units	Field / arbitrary units
1	9
1.5	4
2	2.25
2.5	1.44
3	1