Challenging +1.2 This is a 3D moments problem requiring identification of the center of mass position for a hemisphere (3r/8 from base), setting up moment equilibrium about point A, and resolving forces. While it involves multiple steps and the hemisphere geometry adds complexity beyond basic rigid body problems, the solution path is systematic once the center of mass formula is recalled, making it moderately above average difficulty for A-level mechanics.
2
\includegraphics[max width=\textwidth, alt={}, center]{fb79f949-567c-4dbb-8533-7b7278cad21c-2_839_330_539_906}
\(A B\) is a diameter of a uniform solid hemisphere with centre \(O\), radius 10 cm and weight 12 N . One end of a light inextensible string is attached to the hemisphere at \(B\) and the other end is attached to a fixed point \(C\) of a vertical wall. The hemisphere is in equilibrium with \(A\) in contact with the wall at a point vertically below \(C\). The centre of mass \(G\) of the hemisphere is at the same horizontal level as \(A\), and angle \(A B C\) is a right angle (see diagram). Calculate the tension in the string.
2\\
\includegraphics[max width=\textwidth, alt={}, center]{fb79f949-567c-4dbb-8533-7b7278cad21c-2_839_330_539_906}\\
$A B$ is a diameter of a uniform solid hemisphere with centre $O$, radius 10 cm and weight 12 N . One end of a light inextensible string is attached to the hemisphere at $B$ and the other end is attached to a fixed point $C$ of a vertical wall. The hemisphere is in equilibrium with $A$ in contact with the wall at a point vertically below $C$. The centre of mass $G$ of the hemisphere is at the same horizontal level as $A$, and angle $A B C$ is a right angle (see diagram). Calculate the tension in the string.
\hfill \mbox{\textit{CAIE M2 2009 Q2 [4]}}