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AP Physics 1 · Question of the Day

AP Physics 1 Question of the Day

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Thursday, October 22, 2026

Two masses interact gravitationally. Case A: MM and $2M$ separated by rr. Case B: MM and $2M$ separated by 3r3r. Which case has the larger force?

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Two masses interact gravitationally. Case A: MM and $2M$ separated by rr. Case B: MM and $2M$ separated by 3r3r. Which case has the larger force?

  1. Case B, because the masses are the same in both cases.
  2. Case A, because the distance is smaller. (correct answer)
  3. They are equal because the product M(2M)M(2M) is the same.
  4. Case B, because greater separation increases gravitational attraction.

Explanation: This problem tests understanding of how distance affects gravitational force. Using F = Gm₁m₂/r², both cases have the same masses (M and 2M) but different distances. Case A: F_A = G(M)(2M)/r² = 2GM²/r². Case B: F_B = G(M)(2M)/(3r)² = 2GM²/9r² = (2GM²/r²)/9 = F_A/9. Since Case B has nine times larger denominator due to the distance being tripled and squared, Case A has nine times larger force than Case B. Choice C incorrectly ignores the distance difference, focusing only on the mass product. When comparing gravitational scenarios with the same masses but different distances, the case with smaller distance always has the larger force due to the inverse-square law.