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AS Daily A Level Physics question

2026-02-28 OCR A Dynamics: forces, drag and terminal velocity (Module 3) OCR Physics A (AS) Module 3: Forces and motion — Newton’s laws and equilibrium of forces OCR Physics A (AS) Module 3: Forces in action — friction/drag and terminal velocity (qualitative)

Two solid plastic spheres are geometrically similar and made of the same material. Sphere B has twice the radius of sphere A. Each is dropped from rest in still air and allowed plenty of time to reach a constant terminal speed. Neglect upthrust in air. Which statement must be true about their terminal speeds v_B and v_A?

  1. A A Smaller: v_B < v_A because the larger area gives greater upward drag at any given speed, so the larger sphere settles to a lower speed.
  2. B B Equal: v_B = v_A because they share the same shape and material, so the drag-to-weight ratio is unchanged.
  3. C C Larger: v_B > v_A because the weight rises faster with size than the area does, so a higher speed is required before upward drag can balance the greater weight. (correct)
  4. D D Indeterminate from size alone: v_B could be smaller or larger depending only on the initial acceleration just after release.

Answer

The correct answer is C.

Correct: C — C Larger: v_B > v_A because the weight rises faster with size than the area does, so a higher speed is required before upward drag can balance the greater weight. A Overemphasises area: although the larger area increases drag at a given speed, the larger sphere’s weight (scaling with volume) increases more strongly, so it needs a higher, not lower, terminal speed to achieve force balance (upward drag = downward weight). B Ignores size scaling: same shape/material does not fix terminal speed because weight scales with volume while drag at a given speed scales with area, changing the drag-to-weight balance. C States the correct force-balance reasoning at terminal velocity (net force zero, upward drag balancing greater downward weight), so the larger sphere must reach a higher speed. D Confuses transient with steady state: initial acceleration affects how speed changes early on, but terminal speed is set by the long-time force balance, not by the initial acceleration.

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