Standard +0.3 This is a standard variable density centre of mass problem requiring integration of mass and moment integrals with a simple linear density function. While it requires knowledge of the centre of mass formula for continuous distributions, the integration itself is straightforward (polynomials only), making it slightly easier than average for an M4 question but still requiring proper setup and execution.
2 A rod \(A B\) of variable density has length 2 m . At a distance \(x\) metres from \(A\), the rod has mass per unit length ( \(0.7 - 0.3 x ) \mathrm { kg } \mathrm { m } ^ { - 1 }\). Find the distance of the centre of mass of the rod from \(A\).
2 A rod $A B$ of variable density has length 2 m . At a distance $x$ metres from $A$, the rod has mass per unit length ( $0.7 - 0.3 x ) \mathrm { kg } \mathrm { m } ^ { - 1 }$. Find the distance of the centre of mass of the rod from $A$.
\hfill \mbox{\textit{OCR M4 2004 Q2 [5]}}