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ID: past-exam-of-the-physics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2014/paper-1/a4/solution

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Past exam of the physics course of the year 1 of the natural sciences course of the University of Cambridge / 2014 / Paper 1 / A4 / Solution by

Codex  0 2026-10-20

Converting all lengths to metres gives

d = 3.7276 \times 1 0^{- 5} m

. Logarithmic differentiation gives

\frac{δ d}{d} = \frac{δ F}{F} + 3 \frac{δ L}{L} - \frac{δ E}{E} - \frac{δ w}{w} - 3 \frac{δ t}{t} .

(1)

If the quoted uncertainties are independent standard uncertainties, monomial uncertainty propagation gives

\frac{σ _{d}}{d} = 0.0 1^{2} + 0.0 6^{2} + 0.00 5^{2} + (0.1/9)^{2} + 0.02 5^{2} = 0.0669, d = (37.3 \pm 2.5) μ m .

(2)

If the quoted uncertainties instead mean bounds, the first-order conservative fractional error is

0.111

, giving approximately $37.3 \pm 4.1 μ m$ . The question does not specify their statistical meaning; these two error conventions should not be combined.

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