IB Physics – Data-Based Questions (Paper 1B)

A student measures the length of a wire as $L = (25.0 \pm 0.1)\,\text{cm}$.Calculate the percentage uncertainty in $L$.

Two lengths are measured as $l_1 = (12.4 \pm 0.2)\,\text{cm}$ and $l_2 = (8.6 \pm 0.1)\,\text{cm}$.(a) Calculate the sum $l_1 + l_2$ with its absolute uncertainty.(b) State the rule used for combining uncertainties in a sum.

A wire has diameter $d = (0.32 \pm 0.01)\,\text{mm}$ and length $L = (0.500 \pm 0.001)\,\text{m}$. Its resistance is measured as $R = (1.35 \pm 0.05)\,\Omega$.(a) Calculate the cross-sectional area $A$ of the wire.(b) Calculate the resistivity $\rho = \dfrac{RA}{L}$ of the wire.(c) Determine the percentage uncertainty, and hence the absolute uncertainty, in $\rho$.

A student uses a digital vernier caliper with a resolution of $0.01\,\text{mm}$ to take a single measurement of a rod’s diameter.State the absolute uncertainty that should be recorded, and explain why.

A student times $10$ oscillations of a simple pendulum of length $L = (0.850 \pm 0.002)\,\text{m}$ and finds the period $T = (1.851 \pm 0.006)\,\text{s}$.(a) Use $g = \dfrac{4\pi^2 L}{T^2}$ to calculate a value for $g$.(b) Calculate the percentage uncertainty in $g$.(c) State the absolute uncertainty in $g$, and hence give $g$ with its uncertainty to an appropriate number of significant figures.

Gamma radiation passes through absorbers of thickness $x$ and the intensity $I$ is recorded:$x/\text{cm}$: 0, 2, 4, 6, 8, 10$I/\text{counts s}^{-1}$: 820, 610, 450, 335, 250, 185The intensity follows $I = I_0 e^{-\mu x}$.(a) Explain why plotting $\ln I$ against $x$ should give a straight line, and state the significance of the gradient and the $y$-intercept.(b) Given that the gradient of the best-fit line of $\ln I$ against $x$ is $-0.149\,\text{cm}^{-1}$ and the $y$-intercept is $6.71$, find the attenuation coefficient $\mu$ and the value of $I_0$.(c) Calculate the half-value thickness of the absorber.

In a timing experiment a student measures the period of a single oscillation using a hand-held stopwatch.Suggest one change to the method that would reduce the random uncertainty in the period, and explain why it works.

A student measuring the resistivity of a wire notices that every resistance reading is $0.3\,\Omega$ higher than expected because the ammeter was not zeroed before use.(a) State whether this is a random or a systematic error.(b) Explain the effect this error has on the calculated resistivity, and how the error could be removed.

Small steel spheres of radius $r$ fall at terminal velocity $v$ through a viscous liquid. Data collected:$r/\text{mm}$: 0.5, 1.0, 1.5, 2.0$v/\text{cm s}^{-1}$: 2.1, 8.3, 18.9, 33.5(a) Show that these data are consistent with $v \propto r^2$.(b) The relationship is $v = \dfrac{2r^2(\rho_s-\rho_f)g}{9\eta}$, where $\rho_s = 2500\,\text{kg m}^{-3}$ and $\rho_f = 960\,\text{kg m}^{-3}$. A graph of $v$ against $r^2$ has gradient $8.4\times10^4\,\text{s}^{-1}\,\text{m}^{-1}$ (SI units). Calculate the viscosity $\eta$ of the liquid.

In the pendulum experiment of Question 5, the accepted value of $g$ at the location is $9.81\,\text{m s}^{-2}$.(a) Calculate the percentage difference between the experimental value and the accepted value.(b) State, with a reason, whether the experimental value is consistent with the accepted value.

A student investigates how the period $T$ of a pendulum depends on its length $L$, believing $T = kL^{n}$.$L/\text{m}$: 0.20, 0.40, 0.60, 0.80, 1.00$T/\text{s}$: 0.90, 1.27, 1.55, 1.79, 2.01(a) Explain how plotting $\log T$ against $\log L$ allows $n$ and $k$ to be determined.(b) The best-fit line through $\log T$ vs $\log L$ has gradient $0.498$ and $y$-intercept $0.302$. Determine $n$ and $k$, giving each to an appropriate number of significant figures.(c) State the physical significance of the value of $n$ found.

For the gamma-ray absorption experiment in Question 6, suggest one improvement to the experimental method that would reduce the uncertainty in the measured count rate, and justify your answer.