Edexcel M2 — Question 2 7 marks

Exam BoardEdexcel
ModuleM2 (Mechanics 2)
Marks7
PaperDownload PDF ↗
Mark schemeDownload PDF ↗
TopicCentre of Mass 1
TypeL-shaped or composite rectangular lamina
DifficultyStandard +0.3 This is a standard M2 centre of mass problem requiring decomposition into simple shapes (circles and rectangles), calculation of individual centres of mass, and application of the composite body formula. While it involves multiple components and careful bookkeeping of positive/negative contributions, it follows a routine algorithmic approach with no novel problem-solving required. The 7 marks reflect computational length rather than conceptual difficulty.
Spec6.04c Composite bodies: centre of mass

\includegraphics{figure_2} A key is modelled as a lamina which consists of a circle of radius 3 cm, with a circle of radius 1 cm removed from its centre, attached to a rectangle of length 8 cm and width 1 cm, with a rectangle measuring 3 cm by 1 cm fixed to its end as shown. Calculate the distance of the centre of mass of the key from the line marked \(AB\). [7 marks]

AnswerMarks Guidance
\(8\pi(3) + 8(10) + 3(13 \cdot 5) = (11 + 8\pi)\bar{x}\)M1 M1 A1 A1
\(\bar{x} = (24\pi + 120 \cdot 5) + (8\pi + 11) = 5 \cdot 42\) cmM1 A1 A1 (7 marks)
$8\pi(3) + 8(10) + 3(13 \cdot 5) = (11 + 8\pi)\bar{x}$ | M1 M1 A1 A1 |

$\bar{x} = (24\pi + 120 \cdot 5) + (8\pi + 11) = 5 \cdot 42$ cm | M1 A1 A1 | (7 marks)
\includegraphics{figure_2}

A key is modelled as a lamina which consists of a circle of radius 3 cm, with a circle of radius 1 cm removed from its centre, attached to a rectangle of length 8 cm and width 1 cm, with a rectangle measuring 3 cm by 1 cm fixed to its end as shown.

Calculate the distance of the centre of mass of the key from the line marked $AB$. [7 marks]

\hfill \mbox{\textit{Edexcel M2  Q2 [7]}}