Challenging +1.8 This is a Further Maths M5 question requiring integration to find moment of inertia for a 2D lamina with non-trivial geometry. Students must set up appropriate strip elements, handle the triangular boundary correctly, and integrate with respect to perpendicular distance from the edge. While the technique is standard for M5, the geometric setup and algebraic manipulation make it significantly harder than typical A-level questions.
4. A uniform plane lamina of mass \(m\) is in the shape of an equilateral triangle of side \(2 a\). Find, using integration, the moment of inertia of the lamina about one of its edges.
(9)
4. A uniform plane lamina of mass $m$ is in the shape of an equilateral triangle of side $2 a$. Find, using integration, the moment of inertia of the lamina about one of its edges.\\
(9)\\
\hfill \mbox{\textit{Edexcel M5 Q4 [9]}}