Standard +0.8 This is a standard M4 moment of inertia calculation requiring integration of y² over the lamina area, but involves multiple steps: finding area, density, setting up the double integral (or using the standard formula), and careful algebraic manipulation of the 1/x⁴ terms. The 8-mark allocation reflects substantial working, placing it moderately above average difficulty for requiring both conceptual understanding of lamina moments and technical integration skill.
The region bounded by the \(x\)-axis, the lines \(x = 1\) and \(x = 2\) and the curve \(y = \frac{1}{x^2}\) for \(1 \leq x \leq 2\), is occupied by a uniform lamina of mass 24 kg. The unit of length is the metre. Find the moment of inertia of this lamina about the \(x\)-axis. [8]
The region bounded by the $x$-axis, the lines $x = 1$ and $x = 2$ and the curve $y = \frac{1}{x^2}$ for $1 \leq x \leq 2$, is occupied by a uniform lamina of mass 24 kg. The unit of length is the metre. Find the moment of inertia of this lamina about the $x$-axis. [8]
\hfill \mbox{\textit{OCR M4 2006 Q3 [8]}}