2
\begin{enumerate}[label=(\alph*)]
\item Write down the dimensions of pressure.

The SI unit of pressure is the pascal (Pa). 15 Pa is equivalent to $Q$ newtons per square centimetre.
\item Find the value of $Q$.

Simon thinks the speed, $v$, of sound in a gas is given by the formula\\
$v = k P ^ { x } d ^ { y } V ^ { z }$,\\
where $P$ is the pressure of the gas,\\
$d$ is the density of the gas,\\
$V$ is the volume of the gas,\\
$k$ is a dimensionless constant.
\item Use dimensional analysis to

\begin{itemize}
  \item find the values of $x$ and $y$ and
  \item show that $z = 0$.\\[0pt]
[4]\\
At normal atmospheric pressure the density of air at sea level is $1.29 \mathrm {~kg} \mathrm {~m} ^ { - 3 }$. Under the same conditions the density of helium is $0.166 \mathrm {~kg} \mathrm {~m} ^ { - 3 }$.
\item Given that the speed of sound in air under these conditions is $340 \mathrm {~m} \mathrm {~s} ^ { - 1 }$, use Simon's formula to find the speed of sound in helium under the same conditions.
\end{itemize}
\end{enumerate}

\hfill \mbox{\textit{OCR MEI Further Mechanics Minor 2019 Q2 [8]}}