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A2 Daily A Level Physics question

2026-06-01 OCR A AS Mechanics: Equilibrium and moments OCR-A Module 3.2.1 Forces in action — Moments and turning effects OCR-A Module 3.2.1 Forces in action — Conditions for equilibrium of a rigid body

A uniform 2.0 m wooden shelf of mass 10 kg is hinged to a wall at the left end and held horizontal by a light cable attached at the right end, making 30° above the horizontal. A 15 kg toolbox sits on the shelf initially 1.5 m from the hinge and is then moved to 1.0 m from the hinge. Neglect the shelf’s thickness. Which statement best describes what happens to the cable tension? (Take g ≈ 9.8 m s−2.)

  1. A It increases by about 23% because moving the toolbox closer reduces its lever arm, so the cable must take a larger share of the total weight.
  2. B It decreases by about 23% because the required counterclockwise moment from the cable falls when the toolbox’s distance is reduced from 1.5 m to 1.0 m. (correct)
  3. C It decreases by about 50% because halving the distance to the right end halves the cable’s moment arm.
  4. D It is unchanged because the hinge provides whatever turning effect is needed; the cable only supports vertical weight.

Answer

The correct answer is B.

Correct: B — It decreases by about 23% because the required counterclockwise moment from the cable falls when the toolbox’s distance is reduced from 1.5 m to 1.0 m. Taking moments about the hinge, T sin30° × 2.0 = (15g × x) + (10g × 1.0), so T = 15g x + 10g; T changes from ≈318.5 N (x=1.5 m) to ≈245 N (x=1.0 m), a decrease of about 23%. A Moving the toolbox closer reduces the clockwise moment, so the cable’s required moment (and thus tension) falls, not rises. B This matches the moment balance and quick numbers (≈318.5 N to ≈245 N). C The cable’s moment arm about the hinge stays at 2.0 m; the 50% claim confuses the toolbox shift with the cable’s lever arm. D An ideal hinge provides force but no moment; the cable must supply the balancing moment, so tension does change.

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