Standard +0.8 This is a non-trivial equilibrium problem requiring knowledge that the centre of mass of a uniform cone is at 3h/4 from the vertex, setting up moment equations about point P with the cone tilted at an unusual angle (PQ vertical means axis at arctan(4/20) to horizontal), and resolving forces in two directions. The geometry is more complex than standard equilibrium questions, requiring careful consideration of the force directions and perpendicular distances.
2
\includegraphics[max width=\textwidth, alt={}, center]{5a2248f6-3ef9-4e69-90cf-4d6a2351be14-2_319_908_438_616}
A uniform solid cone has height 20 cm and base radius \(4 \mathrm {~cm} . P Q\) is a diameter of the base of the cone. The cone is held in equilibrium, with \(P\) in contact with a horizontal surface and \(P Q\) vertical, by a force applied at \(Q\). This force has magnitude 3 N and acts parallel to the axis of the cone (see diagram). Calculate the mass of the cone.
2\\
\includegraphics[max width=\textwidth, alt={}, center]{5a2248f6-3ef9-4e69-90cf-4d6a2351be14-2_319_908_438_616}
A uniform solid cone has height 20 cm and base radius $4 \mathrm {~cm} . P Q$ is a diameter of the base of the cone. The cone is held in equilibrium, with $P$ in contact with a horizontal surface and $P Q$ vertical, by a force applied at $Q$. This force has magnitude 3 N and acts parallel to the axis of the cone (see diagram). Calculate the mass of the cone.
\hfill \mbox{\textit{CAIE M2 2010 Q2 [4]}}