Challenging +1.2 This is a moments problem involving a curved uniform object with a non-trivial center of mass calculation. Students must recall that the center of mass of a circular arc is at distance (r sin θ)/θ from the center, apply moment equilibrium about point A, and resolve forces. While requiring multiple steps and knowledge of a specific formula, it follows a standard equilibrium approach with clear geometry, making it moderately above average difficulty for A-level mechanics.
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The diagram shows a uniform object \(A B C\) of weight 3 N in the form of an arc of a circle with centre \(O\) and radius 0.7 m . The angle \(A O C\) is 2 radians. The object rests in equilibrium with \(A\) on a horizontal surface and \(C\) vertically above \(A\). Equilibrium is maintained by a horizontal force of magnitude \(F \mathrm {~N}\) applied at \(C\) in the plane of the object. Calculate \(F\).
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\includegraphics[max width=\textwidth, alt={}, center]{98bbefd8-b3dd-49f1-8591-e939282cb05c-2_448_547_434_799}
The diagram shows a uniform object $A B C$ of weight 3 N in the form of an arc of a circle with centre $O$ and radius 0.7 m . The angle $A O C$ is 2 radians. The object rests in equilibrium with $A$ on a horizontal surface and $C$ vertically above $A$. Equilibrium is maintained by a horizontal force of magnitude $F \mathrm {~N}$ applied at $C$ in the plane of the object. Calculate $F$.
\hfill \mbox{\textit{CAIE M2 2012 Q2 [4]}}