Standard +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.
\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]
\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]}}