\documentclass[compose]{exam-n} \usepackage{graphics} \graphicspath{{fig/}} \begin{document} \begin{question}{20} \author{Reginald Q Whimsy} % Have a blank line here, to check that the question number remains % nicely lined up, even if there are lines between the environment % opening and the text. First, \emph{admire} the restful picture of a spiral in Fig.\ \ref{f:spiral}, included as a graphic. Fully zenned up? Then let us begin\dots. \begin{figure} \ifbigfont \includegraphics[width=\textwidth]{spiral} \else \includegraphics{spiral} \fi \caption{\label{f:spiral}A spiral} \end{figure} \part Show that, under the action of gravity alone, the scale size of the Universe varies according to \begin{equation} \ddot{R}=-\frac{4\pi G \rho_0}{3R^2} \end{equation} \partmarks*{4} and that, consequently, \begin{equation*} \dot{R}^2=-\frac{8\pi G \rho_0}{3R}=-K. \partmarks*{3} \end{equation*} Express $K$ in terms of the present values of the Hubble constant $H_0$ and of the density parameter $\Omega_0$. \partmarks{3} \begin{solution} This can be solved by \emph{remembering} the solution \partmarks{3} \end{solution} \part In the early Universe, the relation between time and temperature has the form \begin{equation*} t=\sqrt{\frac{3c^2}{16\pi G g_{\rm eff}a}}\frac{1}{T^2}, \end{equation*} where $a$ is the radiation constant. Discuss the assumptions leading to this equation, but do not carry out the mathematical derivation. Discuss the meaning of the factor $g_{\rm eff}$ , and find its value just before and after annihilation of electrons and positrons. \partmarks{6} \begin{solution} Before, well, geee; after\dots kazamm! \end{solution} \part Explain how the present-day neutron/proton ratio was established by particle interactions in the Early Universe. How is the ratio of deuterium to helium relevant to the nature of dark matter? It is \emph{crucially vital} to note that Table~\ref{t:dullness} is of absolutely no relevance to this question. \begin{table} \begin{tabular}{r|l} Column 1&and row 1\\ More content&in row 2 \end{tabular} \caption{\label{t:dullness}A remarkably dull table} \end{table} Finis. \begin{questiondata} Hubble's law: $v=H_0 D$ \end{questiondata} \partmarks{4} \begin{solution} Explanations are superfluous; all that is, is. \begin{table} \begin{tabular}{r|l} First rows&are premier\\ subsequent rows&are of secondary interest \end{tabular} \caption{\label{t:dullnessII}A table o'erbrimming with otioseness} \end{table} In addition, Table~\ref{t:dullnessII} adds nothing to the discussion, adds nothing to our understanding of our place in the cosmos, but it \emph{does} contribute slightly to the heat-death of the universe (can you work out how many deuterium nuclei decayed during the typing of this table?). \end{solution} \end{question} \end{document}