For $P=\dfrac{F}{\pi R^2}$ with percentage errors of $\pm2$ in $F$ and $\pm1$ in $R$, the percentage error in $P$ is:
A$\pm1\%$
B$\pm4\%$
C$\pm3\%$
D$\pm5\%$
Answer & Solution
Correct answer: B. $\pm4\%$
1. Take logarithms: $\ln P=\ln F-\ln\pi-2\ln R$.
2. Differentiating gives $\dfrac{\Delta P}{P}=\dfrac{\Delta F}{F}+2\dfrac{\Delta R}{R}$ — the terms ADD when errors are maximised.
3. Multiply through by 100%: $\pm(2\%+2\times1\%)$.
4. That gives $\pm4\%$.
5. Subtracting instead of adding gives $-1\%$, which was the recorded error and shows a misunderstanding of maximising errors.
_Source: NECTA ACSEE 2023 Physics 131/1, Question 1: Measurement_
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