| Exam Board | OCR MEI |
|---|---|
| Module | Further Mechanics Minor (Further Mechanics Minor) |
| Year | 2020 |
| Session | November |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Dimensional Analysis |
| Type | Find exponents with all unknowns |
| Difficulty | Standard +0.3 This is a straightforward dimensional analysis problem requiring students to equate dimensions of speed with powers of pressure and density, then apply the resulting formula to a percentage change calculation. While it requires understanding of dimensions and solving simultaneous equations, it follows a standard template with clear steps and no novel insight required. |
| Spec | 6.01a Dimensions: M, L, T notation6.01d Unknown indices: using dimensions |
| Answer | Marks |
|---|---|
| 2(b) | (1.01)Ξ±(0.995)Ξ²(340) |
| 342.55 (m s-1) | M1 |
| Answer | Marks |
|---|---|
| [2] | 3.1b |
| 2.2b | Correct method for finding new speed |
| Answer | Marks |
|---|---|
| ft their only | With their values |
Question 2:
--- 2(b) ---
2(b) | (1.01)Ξ±(0.995)Ξ²(340)
342.55 (m s-1) | M1
A1ft
[2] | 3.1b
2.2b | Correct method for finding new speed
allow 1 incorrect multiplier.
ft their only | With their values
from (a)
342.55322735β¦
ππππ πΌπΌ ππππππ π½π½2 The speed of propagation, $c$, of a soundwave travelling in air is given by the formula $c = k p ^ { \alpha } d ^ { \beta }$,\\
where
\begin{itemize}
\item $p$ is the air pressure,
\item $d$ is the air density,
\item $k$ is a dimensionless constant.
\begin{enumerate}[label=(\alph*)]
\item Use dimensional analysis to determine the values of $\alpha$ and $\beta$.
\end{itemize}
During a series of experiments the speed of propagation of soundwaves travelling in air is initially recorded as $340 \mathrm {~m} \mathrm {~s} ^ { - 1 }$. At a later time it is found that the air pressure has increased by $1 \%$ and the air density has fallen by $0.5 \%$.
\item Determine, for the later time, the speed of propagation of the soundwaves.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Mechanics Minor 2020 Q2 [7]}}