CAIE M2 2017 November — Question 2 3 marks

Exam BoardCAIE
ModuleM2 (Mechanics 2)
Year2017
SessionNovember
Marks3
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicCentre of Mass 1
TypeComposite solid with hemisphere and cylinder/cone
DifficultyStandard +0.3 This is a straightforward centre of mass problem requiring students to recall that a cone's COM is at h/4 from its base, set up a moments equation with two unknowns, and solve a simple linear equation. The setup is standard and requires no geometric insight beyond textbook formulas.
Spec6.04c Composite bodies: centre of mass6.04e Rigid body equilibrium: coplanar forces

2 A uniform solid cone has height 0.6 m and base radius 0.2 m . A uniform hollow cylinder, open at both ends, has the same dimensions. An object is made by putting the cone inside the cylinder so that the base of the cone coincides with one end of the cylinder (see diagram, which shows a cross-section). The total weight of the object is 60 N and its centre of mass is 0.25 m from the base of the cone. Calculate the weight of the cone.

Question 2:
AnswerMarks Guidance
AnswerMarks Guidance
\(0.15W + 0.3(60 - W) = 0.25 \times 60\)M1A1 Attempts to take moments about the base of the cone. \(W\) = weight of the cone.
\(W = 20\text{ N}\)A1
Total3
## Question 2:

| Answer | Marks | Guidance |
|--------|-------|----------|
| $0.15W + 0.3(60 - W) = 0.25 \times 60$ | M1A1 | Attempts to take moments about the base of the cone. $W$ = weight of the cone. |
| $W = 20\text{ N}$ | A1 | |
| **Total** | **3** | |

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2

A uniform solid cone has height 0.6 m and base radius 0.2 m . A uniform hollow cylinder, open at both ends, has the same dimensions. An object is made by putting the cone inside the cylinder so that the base of the cone coincides with one end of the cylinder (see diagram, which shows a cross-section). The total weight of the object is 60 N and its centre of mass is 0.25 m from the base of the cone. Calculate the weight of the cone.\\

\hfill \mbox{\textit{CAIE M2 2017 Q2 [3]}}