Graphical Analysis with Uncertainties — practice questions

A student's steepest acceptable line has gradient $2.45$ and their shallowest has gradient $2.05$.

Calculate the uncertainty in the gradient, and state the gradient if the line of best fit gives $2.24$.

A student plots $T$ against $L$ with vertical error bars of $\pm 0.02$ s on periods of about $1.5$ s, then linearises by plotting $T^2$.

Calculate the error bar to use on the $T^2$ axis, and explain why it is not simply $\pm 0.02$.

A student draws error bars, then draws their steepest and shallowest lines by pivoting both about the leftmost data point.

Evaluate this method and explain what effect it has on the uncertainty they obtain.

A theory predicts a linearised graph should pass through the origin.

State what a significant non-zero intercept indicates.

Explain why a systematic error usually changes the intercept of a linearised graph but not its gradient, and explain why this matters for a value calculated from the gradient.

A student measuring the resistance of a wire plots resistance $R$ against length $l$, expecting a line through the origin, and obtains a positive intercept of $0.8 \pm 0.1$ Ω.

Discuss possible causes of this intercept, and evaluate whether it invalidates their conclusion about the relationship between $R$ and $l$.