A model of a compact spherical source predicts that field strength g varies as 1/r² outside the source. The (distance from centre in units of 1000 km, field strength in N/kg) measurements are (1, 8), (2, 2), (3, 0.89), (4, 0.5). Test the model by calculating g r² with the distance numbers as tabulated. For this exercise, call a record consistent when every product is within 5% of the first product. Identify any inconsistent readings and explain one measurement or model limitation. All locations are outside the source.

Question

Accepted Answer

Scaled products 8, 8, 8.01, 8; consistent with the stated 5% comparison rule. Agreement supports this model over the measured range only. If g is proportional to 1/r², multiplying each field strength by the square of its centre distance should remove the distance dependence. The common distance scale factor does not affect this consistency test. The four scaled products are 8 × 1² = 8; 2 × 2² = 8; 0.89 × 3² = 8.01; 0.5 × 4² = 8. They would each be multiplied by 10¹² to express g r² using metres. Use the first product 8 as the task's reference. The absolute percentage departures are 0, 0, 0.125, 0%, so the record passes the explicitly supplied 5% rule. These measurements support an inverse-square dependence over the sampled region, but other models might also fit a limited or rounded dataset. Check that distance is measured from the source centre, calibrate the force sensor and repeat the measurements. The 5% rule is a classroom decision threshold, not a statistical confidence interval or proof that all other fields are absent.

A weak-field body

What a complete response should do

Supplied field measurements

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Supplied field measurements — supplied values
Centre distance (1000 km)	Field strength (N/kg)
1	8
2	2
3	0.89
4	0.5