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0580/22 May/Jun 2021, Question 21: Inverse Proportion: y = k/x

Cambridge IGCSE Mathematics 0580 · Paper 22 (Extended) · Calculator · 3 marks

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The question, in short

Force F between magnets varies inversely with d squared; given F = 48 when d = 1.5, find F as a formula in d, then find the factor n when distance doubles.

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Part (a) · 2 marks

Use the inverse-square relationship and the given pair of values to derive a formula giving F in terms of d.

  1. 1F = k/d²
  2. 248 = k/1.5², so k = 48 × 2.25 = 108
  3. 3F = 108/d²

Answer108/d²

Part (b) · 1 mark

Determine the multiplier n that relates the new force to the original when the separation is doubled.

  1. 1New F = 108/(2d)² = 108/(4d²)
  2. 2= 1/4 × 108/d², so n = 1/4

Answer1/4 or 0.25

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Also searched as: 0580/22/M/J/21 · 0580_s21_qp_22 · 0580 s21 22 · question 21.
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