| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2014 |
| Session | November |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Centre of Mass 1 |
| Type | Composite solid with hemisphere and cylinder/cone |
| Difficulty | Standard +0.3 This is a standard centre of mass problem requiring application of standard formulas for cylinder and hemisphere centres of mass, followed by a routine equilibrium condition. The composite centre of mass calculation is straightforward (5 marks), and the tilting equilibrium condition (tan α = base radius / height to COM) is a direct application of a standard result (3 marks). Slightly above average difficulty due to 3D geometry and two-part structure, but all techniques are standard textbook exercises. |
| Spec | 6.04c Composite bodies: centre of mass6.04e Rigid body equilibrium: coplanar forces |
| Answer | Marks |
|---|---|
| (ii) | ABCF area = 0.64 and CDE = 0.36 |
| Answer | Marks |
|---|---|
| T = 5.5 | B1 |
| Answer | Marks |
|---|---|
| A1 [3] | Both areas correct |
| Answer | Marks | Guidance |
|---|---|---|
| Page 5 | Mark Scheme | Syllabus |
| Cambridge International A Level – October/November 2014 | 9709 | 51 |
Question 4:
--- 4 (i)
(ii) ---
4 (i)
(ii) | ABCF area = 0.64 and CDE = 0.36
0.4 1.8
(0.64 + 0.36)d = 0.64× + 0.36×(0.4 + )
2 3
d = 0.488 m AG
0.488 × 100 = 1.6T
T = 30.5 N
(0.488 – 0.4) × 100 = 1.6T
T = 5.5 | B1
M1
A1
A1
[4]
M1
A1
A1 [3] | Both areas correct
Table of moments idea
All terms correct
Either limiting case
(no turning about A)
(no turning about F)
Page 5 | Mark Scheme | Syllabus | Paper
Cambridge International A Level – October/November 2014 | 9709 | 51\includegraphics{figure_4}
The diagram shows the cross-section of a uniform solid consisting of a cylinder of radius $0.4$ m and height $1.5$ m with a hemisphere of radius $0.4$ m on top.
\begin{enumerate}[label=(\roman*)]
\item Find the distance of the centre of mass above the base of the cylinder. [5]
\item The solid can just rest in equilibrium on a plane inclined at angle $\alpha$ to the horizontal. Find $\alpha$. [3]
\end{enumerate}
\hfill \mbox{\textit{CAIE M2 2014 Q4 [8]}}