Challenging +1.2 This is a standard M4 moment of inertia calculation requiring the formula for MOI of a solid of revolution about the x-axis (I = ∫ρπy⁴/2 dx) with straightforward integration of x⁸. While it's a Further Maths topic making it inherently harder than Core modules, it's a direct application of a standard formula with no conceptual complications—typical textbook exercise for students who have learned this technique.
2 A uniform solid of revolution is formed by rotating the region bounded by the \(x\)-axis, the line \(x = 1\) and the curve \(y = x ^ { 2 }\) for \(0 \leqslant x \leqslant 1\), about the \(x\)-axis. The units are metres, and the density of the solid is \(5400 \mathrm {~kg} \mathrm {~m} ^ { - 3 }\). Find the moment of inertia of this solid about the \(x\)-axis.
2 A uniform solid of revolution is formed by rotating the region bounded by the $x$-axis, the line $x = 1$ and the curve $y = x ^ { 2 }$ for $0 \leqslant x \leqslant 1$, about the $x$-axis. The units are metres, and the density of the solid is $5400 \mathrm {~kg} \mathrm {~m} ^ { - 3 }$. Find the moment of inertia of this solid about the $x$-axis.
\hfill \mbox{\textit{OCR M4 2002 Q2 [5]}}