Moderate -0.8 This is a straightforward application of the centre of mass formula for a system of particles. Students need to use the formula $\bar{x} = \frac{\sum m_i x_i}{\sum m_i}$ (and similarly for $\bar{y}$), treating the lamina as a single particle at its given centre of mass. The calculation involves basic arithmetic with given coordinates and masses—no problem-solving insight or geometric reasoning required, making it easier than average.
2 A piece of modern art is modelled as a uniform lamina and three particles. The diagram shows the lamina, the three particles \(A , B\) and \(C\), and the \(x\) - and \(y\)-axes.
\includegraphics[max width=\textwidth, alt={}, center]{06b431ca-d3a8-46d6-b9f8-bac08d3fd51e-2_875_1004_1414_502}
The lamina, which is fixed in the \(x - y\) plane, has mass 10 kg and its centre of mass is at the point (12, 9).
The three particles are attached to the lamina.
Particle \(A\) has mass 3 kg and is at the point (15, 6).
Particle \(B\) has mass 1 kg and is at the point ( 7,14 ).
Particle \(C\) has mass 6 kg and is at the point ( 8,7 ).
Find the coordinates of the centre of mass of the piece of modern art.
2 A piece of modern art is modelled as a uniform lamina and three particles. The diagram shows the lamina, the three particles $A , B$ and $C$, and the $x$ - and $y$-axes.\\
\includegraphics[max width=\textwidth, alt={}, center]{06b431ca-d3a8-46d6-b9f8-bac08d3fd51e-2_875_1004_1414_502}
The lamina, which is fixed in the $x - y$ plane, has mass 10 kg and its centre of mass is at the point (12, 9).
The three particles are attached to the lamina.\\
Particle $A$ has mass 3 kg and is at the point (15, 6).\\
Particle $B$ has mass 1 kg and is at the point ( 7,14 ).\\
Particle $C$ has mass 6 kg and is at the point ( 8,7 ).\\
Find the coordinates of the centre of mass of the piece of modern art.
\hfill \mbox{\textit{AQA M2 2010 Q2 [6]}}