Standard +0.3 This is a straightforward moments equilibrium problem requiring taking moments about the hinge point A to find the center of mass position. It involves standard mechanics techniques (resolving the force, applying moment equilibrium) with clear given values and a single unknown, making it slightly easier than average for A-level mechanics.
\includegraphics{figure_2}
A non-uniform rod \(AB\) of length \(0.5 \text{ m}\) and weight \(8 \text{ N}\) is freely hinged to a fixed point at \(A\). The rod makes an angle of \(30°\) with the horizontal with \(B\) above the level of \(A\). The rod is held in equilibrium by a force of magnitude \(12 \text{ N}\) acting in the vertical plane containing the rod at an angle of \(30°\) to \(AB\) applied at \(B\) (see diagram). Find the distance of the centre of mass of the rod from \(A\). [3]
\includegraphics{figure_2}
A non-uniform rod $AB$ of length $0.5 \text{ m}$ and weight $8 \text{ N}$ is freely hinged to a fixed point at $A$. The rod makes an angle of $30°$ with the horizontal with $B$ above the level of $A$. The rod is held in equilibrium by a force of magnitude $12 \text{ N}$ acting in the vertical plane containing the rod at an angle of $30°$ to $AB$ applied at $B$ (see diagram). Find the distance of the centre of mass of the rod from $A$. [3]
\hfill \mbox{\textit{CAIE M2 2018 Q2 [3]}}