Standard +0.3 This is a standard M2 moments problem requiring identification of the center of mass of a triangular lamina (at 1/3 from each side), taking moments about the hinge point A, and solving for tension. The geometry is straightforward with a right-angled triangle and given angle. While it requires multiple steps (finding center of mass position, resolving perpendicular distances, applying moment equilibrium), these are routine techniques for M2 students with no novel insight needed. Slightly easier than average due to the clean numbers and standard setup.
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A uniform right-angled triangular lamina \(A B C\) with sides \(A B = 12 \mathrm {~cm} , B C = 9 \mathrm {~cm}\) and \(A C = 15 \mathrm {~cm}\) is freely suspended from a hinge at its vertex \(A\). The lamina has mass 2 kg and is held in equilibrium with \(A B\) horizontal by means of a string attached to \(B\). The string is at an angle of \(30 ^ { \circ }\) to the horizontal (see diagram). Calculate the tension in the string.
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\includegraphics[max width=\textwidth, alt={}, center]{dd23f4a8-f7e7-4f80-bad6-7e9ec21565fc-2_465_643_495_749}
A uniform right-angled triangular lamina $A B C$ with sides $A B = 12 \mathrm {~cm} , B C = 9 \mathrm {~cm}$ and $A C = 15 \mathrm {~cm}$ is freely suspended from a hinge at its vertex $A$. The lamina has mass 2 kg and is held in equilibrium with $A B$ horizontal by means of a string attached to $B$. The string is at an angle of $30 ^ { \circ }$ to the horizontal (see diagram). Calculate the tension in the string.
\hfill \mbox{\textit{OCR M2 2009 Q2 [4]}}