| Exam Board | AQA |
|---|---|
| Module | M3 (Mechanics 3) |
| Year | 2010 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Dimensional Analysis |
| Type | Derive dimensions from formula |
| Difficulty | Moderate -0.8 This is a straightforward dimensional analysis problem requiring only substitution of known dimensions into a formula and algebraic manipulation to isolate C. It's more routine than average A-level questions since it involves direct application of a standard technique with no problem-solving insight needed, though it does require careful bookkeeping of dimensions. |
| Spec | 6.01a Dimensions: M, L, T notation6.01b Units vs dimensions: relationship6.01c Dimensional analysis: error checking6.01d Unknown indices: using dimensions |
I don't see any mark scheme content provided in your message. You've indicated "Question 1:" followed by just "1", but there's no actual marking guidance, criteria, or annotations to clean up.
Could you please provide the full extracted mark scheme content that you'd like me to format?1 A tank containing a liquid has a small hole in the bottom through which the liquid escapes. The speed, $u \mathrm {~m} \mathrm {~s} ^ { - 1 }$, at which the liquid escapes is given by
$$u = C V \rho g$$
where $V \mathrm {~m} ^ { 3 }$ is the volume of the liquid in the tank, $\rho \mathrm { kg } \mathrm { m } ^ { - 3 }$ is the density of the liquid, $g$ is the acceleration due to gravity and $C$ is a constant.
By using dimensional analysis, find the dimensions of $C$.\\
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\hfill \mbox{\textit{AQA M3 2010 Q1 [5]}}