| Exam Board | OCR |
|---|---|
| Module | Further Mechanics AS (Further Mechanics AS) |
| Session | Specimen |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Dimensional Analysis |
| Type | Find exponents with all unknowns |
| Difficulty | Standard +0.3 This is a standard dimensional analysis question requiring systematic equation setup and solving simultaneous equations for powers. Part (i) is trivial recall, parts (ii-iii) follow a well-established method taught in Further Mechanics, and part (iv) requires basic physical reasoning about missing variables (likely mass). Slightly above average due to the multi-step nature and need for physical insight in the final part, but this is a textbook application of dimensional analysis. |
| Spec | 6.01a Dimensions: M, L, T notation6.01d Unknown indices: using dimensions |
| Answer | Marks | Guidance |
|---|---|---|
| 3 | (i) | (cid:85)(cid:32)ML(cid:16)3 |
| [1] | 1.2 | Allow ML(cid:16)3 |
| 3 | (ii) | T (cid:32) (cid:11) ML(cid:16)3(cid:12)(cid:68)(cid:11) LT(cid:16)2(cid:12)(cid:69)(cid:11) L2(cid:12)(cid:74) (cid:32)M(cid:68)L(cid:16)3(cid:68)(cid:14)(cid:69)(cid:14)2(cid:74)T(cid:16)2(cid:69) |
| Answer | Marks |
|---|---|
| 4 | M1 |
| Answer | Marks |
|---|---|
| [4] | 3.3 |
| Answer | Marks |
|---|---|
| 1.1 | For (cid:68)(cid:32)0 |
| Answer | Marks |
|---|---|
| (iii) | 1 1 |
| Answer | Marks |
|---|---|
| 2.76 | M1 |
| Answer | Marks |
|---|---|
| [2] | i |
| Answer | Marks | Guidance |
|---|---|---|
| 3.5c | Substituting values into their equation for | |
| T | C(cid:32)2.755472... | |
| 3 | (iv) | e.g. According to this model the period isp |
| Answer | Marks |
|---|---|
| e.g. Because (cid:68)(cid:32)0 | e |
| Answer | Marks |
|---|---|
| [2] | 2.2b |
| 3.5b | e.g. It is possible that the period is |
Question 3:
3 | (i) | (cid:85)(cid:32)ML(cid:16)3 | B1
[1] | 1.2 | Allow ML(cid:16)3
3 | (ii) | T (cid:32) (cid:11) ML(cid:16)3(cid:12)(cid:68)(cid:11) LT(cid:16)2(cid:12)(cid:69)(cid:11) L2(cid:12)(cid:74) (cid:32)M(cid:68)L(cid:16)3(cid:68)(cid:14)(cid:69)(cid:14)2(cid:74)T(cid:16)2(cid:69)
M:(cid:68)(cid:32)0
L:(cid:16)3(cid:68)(cid:14)(cid:69)(cid:14)2(cid:74)(cid:32)0
T:(cid:16)2(cid:69)(cid:32)1
1
(cid:69)(cid:32)(cid:16)
2
1
(cid:74)(cid:32)
4 | M1
B1
M1
A1
[4] | 3.3
1.1
3.4
1.1 | For (cid:68)(cid:32)0
n
e
Setting up equations and solving
simultaneously to find (cid:69) and (cid:74)
m
For β and (cid:74) correct
(iii) | 1 1
(cid:16)
T (cid:32)Cg 2A4
2.76 | M1
A1
[2] | i
c1.1
3.5c | Substituting values into their equation for
T | C(cid:32)2.755472...
3 | (iv) | e.g. According to this model the period isp
independent of the density
S
e.g. Because (cid:68)(cid:32)0 | e
*E1
dep*E1
[2] | 2.2b
3.5b | e.g. It is possible that the period is
dependent on another (unknown) quantity
e.g. because the value of C may depend
on a variable that was not considered
--- 3(i) ---
3(i)
--- 3(ii) ---
3(ii)
t
f
a
r
D
--- 3(iii) ---
3(iii)
--- 3(iv) ---
3(iv)
t
f\begin{enumerate}[label=(\roman*)]
\item Write down the dimension of density. [1]
\end{enumerate}
The workings of an oil pump consist of a right, solid cylinder which is partially submerged in oil. The cylinder is free to oscillate along its central axis which is vertical. If the base area of the pump is $0.4 \, \text{m}^2$ and the density of the oil is $920 \, \text{kg m}^{-3}$ then the period of oscillation of the pump is 0.7 s.
A student assumes that the period of oscillation of the pump is dependent only on the density of the oil, $\rho$, the acceleration due to gravity, $g$, and the surface area, $A$, of the circular base of the pump. The student attempts to test this assumption by stating that the period of oscillation, $T$, is given by $T = C\rho^{\alpha} g^{\beta} A^{\gamma}$ where $C$ is a dimensionless constant.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item Use dimensional analysis to find the values of $\alpha$, $\beta$ and $\gamma$. [4]
\item Hence give the value of $C$ to 3 significant figures. [2]
\item Comment, with justification, on the assumption made by the student that the formula for the period of oscillation of the pump was dependent on only $\rho$, $g$ and $A$. [2]
\end{enumerate}
\hfill \mbox{\textit{OCR Further Mechanics AS Q3 [9]}}