IB DP Physics Mock Exam SL Paper 1B Set 4 - 2025 Syllabus

(a)
Measurements are taken at different places to check for uniformity (such as variations in diameter or thickness) or to minimize the impact of random uncertainties by calculating an average .

(b)
(i) A metre ruler or a measuring tape with millimeter graduations is suitable, provided it is at least \(50\,cm\) long .
(ii) A micrometer screw gauge or a Vernier caliper should be used .

(c)
(i) The reading of \(0.26\,mm\) is considered an outlier and should be discarded. The mean of the remaining five readings is:
\(\frac{0.18 + 0.20 + 0.21 + 0.22 + 0.18}{5} = \frac{0.99}{5} = 0.198\,mm \approx 0.2\,mm\).
(ii) The range of the valid data is \(0.22 – 0.18 = 0.04\,mm\). The absolute uncertainty is half the range: \(\frac{0.04}{2} = 0.02\,mm\) .
The fractional uncertainty is:
\(\frac{0.02}{0.20} = 0.1 \text{ (or } 10\% \text{)}\) .
(iii) The fractional uncertainty in length is:
\(\frac{2}{462} \approx 0.004 \text{ (or } 0.4\% \text{)}\).

(d)
First, calculate the resistivity \(\rho\). Using the mean diameter \(d = 0.20\,mm = 2.0 \times 10^{-4}\,m\), the cross-sectional area is \(A = \pi (\frac{d}{2})^2\).
\(\rho = \frac{RA}{L} = \frac{13.7 \times \pi \times (1.0 \times 10^{-4})^2}{0.462} \approx 9.3 \times 10^{-7}\,\Omega m\) .

Determine the total fractional uncertainty in \(\rho\):
\(\frac{\Delta \rho}{\rho} = \frac{\Delta R}{R} + \frac{\Delta L}{L} + 2\left( \frac{\Delta d}{d} \right)\)
\(\frac{\Delta \rho}{\rho} = 0.015 + 0.004 + 2(0.1) = 0.219\) (or approx \(0.22\)) .
Calculate the absolute uncertainty \(\Delta \rho\):
\(\Delta \rho = 0.22 \times 9.3 \times 10^{-7} \approx 2.0 \times 10^{-7}\,\Omega m\) .

Final Answer:
\(\rho = (9 \pm 2) \times 10^{-7}\,\Omega m\).