| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2017 |
| Session | June |
| Marks | 7 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Centre of Mass 1 |
| Type | Solid with removed cylinder or hemisphere from solid |
| Difficulty | Standard +0.3 This is a straightforward centre of mass problem requiring standard composite body techniques. Students apply the given formula, use the principle of subtraction for the hollow object, then use the composite body formula with given information to find the weight of H. All steps are routine applications of memorized methods with no novel problem-solving required. |
| Spec | 6.04c Composite bodies: centre of mass6.04d Integration: for centre of mass of laminas/solids |
| Answer | Marks |
|---|---|
| 3(i) | 3 3 |
| Answer | Marks |
|---|---|
| 8 8 | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| 8 | M1A1 | Take moments about O |
| X = 0.225 m | A1 | |
| Total: | 4 |
| Answer | Marks | Guidance |
|---|---|---|
| 3(ii) | 24 × 0.225 + W(3 × 0.28 / 8) = (24 + W) × 0.15 | M1A1 |
| Answer | Marks |
|---|---|
| W = 40 N | A1 |
| Total: | 3 |
Question 3:
--- 3(i) ---
3(i) | 3 3
CofM of hemisphere = × 0.56 or × 0.28
8 8 | B1
2 2 2 3 2
[ π × 0.563– π × 0.283]X = π × 0.563 × × 0.56 – π × 0.283×
3 3 3 8 3
3
× 0.28
8 | M1A1 | Take moments about O
X = 0.225 m | A1
Total: | 4
--- 3(ii) ---
3(ii) | 24 × 0.225 + W(3 × 0.28 / 8) = (24 + W) × 0.15 | M1A1 | Attempts to take moments about O
W = weight of uniform hemi-sphere
W = 40 N | A1
Total: | 3\includegraphics{figure_2}
An object is made from a uniform solid hemisphere of radius $0.56$ m and centre $O$ by removing a hemisphere of radius $0.28$ m and centre $O$. The diagram shows a cross-section through $O$ of the object.
\begin{enumerate}[label=(\roman*)]
\item Calculate the distance of the centre of mass of the object from $O$. [4]
[The volume of a hemisphere is $\frac{2}{3}\pi r^3$.]
\item Calculate the weight of $H$. [3]
\end{enumerate}
The object has weight $24$ N. A uniform hemisphere $H$ of radius $0.28$ m is placed in the hollow part of the object to create a non-uniform hemisphere with centre $O$. The centre of mass of the non-uniform hemisphere is $0.15$ m from $O$.
\hfill \mbox{\textit{CAIE M2 2017 Q3 [7]}}