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AS Daily A Level Physics question

2025-12-06 OCR A Upthrust and Archimedes’ principle (M3.1.3) 3.2.4(c)

Which statement must be true when a 2000 kg dayboat floating at rest in freshwater (density 1000 kg m−3) moves into seawater (density 1025 kg m−3) with the same load? Consider the change in the submerged volume of the hull.

  1. A It increases by about 2.5%, because the boat needs more displaced water to balance its weight in denser seawater.
  2. B It stays the same, because the boat’s mass and weight are unchanged.
  3. C It decreases by roughly 2.4%, since denser water requires proportionally less volume to provide the same upthrust. (correct)
  4. D It decreases by about 5%, due to both higher density and reduced draft acting together.

Answer

The correct answer is C.

Correct: C — It decreases by roughly 2.4%, since denser water requires proportionally less volume to provide the same upthrust. A The sign is wrong: for a floating object the weight is constant, so when fluid density rises by about 2.5% the required displaced volume must fall (V ∝ 1/ρ). B Constant mass does not imply constant displaced volume; the volume adjusts so that the upthrust equals the weight. C Using the ratio V2/V1 = ρ1/ρ2 = 1000/1025 ≈ 0.976, the submerged volume falls by about 2.4%. D This double-counts effects; only the change in fluid density matters, giving about a 2.4% decrease, not 5%.

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