Standard +0.8 This problem requires finding the centre of mass of a cone (h/4 from base), applying toppling conditions using moments about the contact point, and solving a trigonometric inequality involving the geometry of the tilted cone. It combines 3D geometry, centre of mass knowledge, and stability analysis—more demanding than routine mechanics questions but uses standard M2 techniques.
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\includegraphics[max width=\textwidth, alt={}, center]{a20a6641-d771-4c89-b40f-168a0c61f99d-2_552_604_264_772}
A uniform solid cone has vertical height 28 cm and base radius 6 cm . The cone is held with a point of the circumference of its base in contact with a horizontal table, and with the base making an angle of \(\theta ^ { \circ }\) with the horizontal (see diagram). When the cone is released, it moves towards the equilibrium position in which its base is in contact with the table. Show that \(\theta < 40.6\), correct to 1 decimal place.
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\includegraphics[max width=\textwidth, alt={}, center]{a20a6641-d771-4c89-b40f-168a0c61f99d-2_552_604_264_772}
A uniform solid cone has vertical height 28 cm and base radius 6 cm . The cone is held with a point of the circumference of its base in contact with a horizontal table, and with the base making an angle of $\theta ^ { \circ }$ with the horizontal (see diagram). When the cone is released, it moves towards the equilibrium position in which its base is in contact with the table. Show that $\theta < 40.6$, correct to 1 decimal place.
\hfill \mbox{\textit{CAIE M2 2005 Q1 [3]}}