Combining uncertainties

Sample questions

Original practice questions written in the style of the exam.

1. Question 14 marks

   A student determines the density of a metal cylinder using these measurements:

   Quantity	Measurement
   mass $m$	$45.2 \pm 0.1\,\text{g}$
   diameter $d$	$2.00 \pm 0.01\,\text{cm}$
   length $L$	$5.00 \pm 0.05\,\text{cm}$

   Calculate the density in $\text{kg m}^{-3}$ and its absolute uncertainty.

   Mark scheme

   • $\rho = \dfrac{m}{\pi (d/2)^2 L} = \dfrac{45.2}{\pi \times 1.00^2 \times 5.00} = 2.88\,\text{g cm}^{-3} = 2880\,\text{kg m}^{-3}$ (1)