| Exam Board | OCR MEI |
|---|---|
| Module | Further Mechanics Minor (Further Mechanics Minor) |
| Year | 2022 |
| Session | June |
| Marks | 6 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Dimensional Analysis |
| Type | Derive dimensions from formula |
| Difficulty | Standard +0.3 This is a straightforward dimensional analysis question requiring students to convert units to MLT form and equate powers. Part (a) is direct substitution, and part (b) involves setting up and solving three simultaneous equations—standard Further Mechanics technique with no novel insight required. |
| Spec | 6.01a Dimensions: M, L, T notation6.01b Units vs dimensions: relationship6.01c Dimensional analysis: error checking6.01d Unknown indices: using dimensions |
| Answer | Marks | Guidance |
|---|---|---|
| 1 | (a) | F o r c e = M a s s A c c e le r a t i o n = M L T − 2 |
| Answer | Marks | Guidance |
|---|---|---|
| G=MLT −2L2M −2 =L3M −1T −2 | B1 | 1.1 |
| Answer | Marks | Guidance |
|---|---|---|
| (b) | L T 1 ( L 3 M 1 T 2 ) M L − = − − | M1 |
| Answer | Marks | Guidance |
|---|---|---|
| 3+=1,−+=0,−2=−1 | M1 | 1.1 |
| 12 = | A1 cao | 1.1 |
| Answer | Marks | Guidance |
|---|---|---|
| 2 2 | A1 cao | 1.1 |
Question 1:
1 | (a) | F o r c e = M a s s A c c e le r a t i o n = M L T − 2 | B1 | 1.2 | Can be implied by correct
dimensions for G
G=MLT −2L2M −2 =L3M −1T −2 | B1 | 1.1
[2]
(b) | L T 1 ( L 3 M 1 T 2 ) M L − = − − | M1 | 1.1 | Substituting their dimensions for G
and correct dimensions for v into
given equation
3+=1,−+=0,−2=−1 | M1 | 1.1 | Setting up all three equations
12 = | A1 cao | 1.1
= 1 =−1
,
2 2 | A1 cao | 1.1
[4]1 Newton's gravitational constant, $G$, is approximately $6.67 \times 10 ^ { - 11 } \mathrm {~N} \mathrm {~m} ^ { 2 } \mathrm {~kg} ^ { - 2 }$.
\begin{enumerate}[label=(\alph*)]
\item Find the dimensions of $G$.
The escape velocity, $v$, of a body from a planet's surface, is given by the formula $\mathrm { v } = \mathrm { kG } ^ { \alpha } \mathrm { M } ^ { \beta } \mathrm { r } ^ { \gamma }$,\\
where $M$ is the planet's mass, $r$ is the planet's radius and $k$ is a dimensionless constant.
\item Use dimensional analysis to find $\alpha , \beta$ and $\gamma$.
\end{enumerate}
\hfill \mbox{\textit{OCR MEI Further Mechanics Minor 2022 Q1 [6]}}