Physics 9702 · AS & A Level · Errors and uncertainties
Errors and uncertainties — practice question
For a liquid moving through a narrow pipe of length $L$ and radius $r$, the flow rate $Q$ is defined by $Q = \frac{\alpha r^4}{L}$, where $\alpha$ is constant. An experiment is performed to find the value of $\alpha$. The experiment data are given in Table 1.1.
(a)[1]
Use the information in Table 1.1 to demonstrate that the SI base unit of $\alpha$ is $\text{s}^{-1}$.
(b)[1]
Show that the percentage uncertainty in $\alpha$ is $15\%$.
(c)[3]
Calculate $\alpha$ together with its absolute uncertainty. Give your answer to an appropriate number of significant figures. $\alpha = (\ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots \pm \ldots\ldots\ldots\ldots\ldots\ldots\ldots\ldots) \times 10^{7}\,\text{s}^{-1}$.
Worked solution & mark scheme
This 5-mark question has a full step-by-step worked solution and mark scheme. One marking point: “SI base unit of $\alpha$ obtained as $\text{m}^3\,\text{s}^{-1} \times \text{m} / \text{m}^4 = \text{s}^{-1}$” …