A-Level Physics May/June 2025 Q5(b)(i): Determine the cross-sectional area of the wire.

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  The Young modulus $E$ is given by the formula: $E = \frac{FL}{Ax}$

  Rearranging for the cross-sectional area $A$: $A = \frac{FL}{Ex}$

  Substitute the given values: $F = 500$ N $L = 0.81$ m $E = 95 \text{ GPa} = 95 \times 10^9$ Pa $x = 4.0 \text{ mm} = 4.0 \times 10^{-3}$ m

  $A = \frac{500 \times 0.81}{(95 \times 10^9) \times (4.0 \times 10^{-3})}$

  $A = 1.0657... \times 10^{-6} \text{ m}^2$

  $A \approx 1.1 \times 10^{-6} \text{ m}^2$ (to 2 s.f.)

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  How the marks are awarded

  • C1 — Correctly rearranging the Young modulus formula to make cross-sectional area (A) the subject, as shown in the step '$A = FL / Ex$'.
  • C1 — Correct substitution of all values for force, length, Young modulus, and extension into the rearranged formula, including correct unit conversions for GPa and mm.
  • A1 — Calculating the final correct answer of '1.1 x 10⁻⁶ m²'. The answer must be to two significant figures and include the correct unit.

  Common mistakes

  • Incorrectly rearranging the Young modulus formula, for example getting $A = Ex / FL$, which leads to an incorrect answer.
  • Forgetting to convert units before substitution, such as using E = 95 instead of 95 x 10⁹ Pa, or x = 4.0 instead of 4.0 x 10⁻³ m.
  • Providing the final answer to an inappropriate number of significant figures, such as writing the full calculator display or rounding to one significant figure.
  • If reading from a graph, picking a pair of force and extension values that do not correspond to the same point on the line.

  Examiner tip: Always write down the base formula first, then clearly show your algebraic rearrangement before substituting any numbers to minimise errors and secure method marks.

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