| Exam Board | OCR |
|---|---|
| Module | M2 (Mechanics 2) |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Centre of Mass 1 |
| Type | Cone stability and toppling conditions |
| Difficulty | Standard +0.3 This is a straightforward toppling problem requiring knowledge that a cone topples when the vertical line through its center of mass passes outside the base. Students need to recall that the center of mass of a uniform solid cone is at h/4 from the base, then apply basic trigonometry (tan 24° = r/5). Part (ii) is trivial comparison. Slightly easier than average due to being a standard textbook application with clear setup. |
| Spec | 6.04e Rigid body equilibrium: coplanar forces |
A uniform solid cone has vertical height 20 cm and base radius $r$ cm. It is placed with its axis vertical on a rough horizontal plane. The plane is slowly tilted until the cone topples when the angle of inclination is $24°$ (see diagram).
\includegraphics{figure_1}
\begin{enumerate}[label=(\roman*)]
\item Find $r$, correct to 1 decimal place. [4]
\end{enumerate}
A uniform solid cone of vertical height 20 cm and base radius 2.5 cm is placed on the plane which is inclined at an angle of $24°$.
\begin{enumerate}[label=(\roman*)]
\setcounter{enumi}{1}
\item State, with justification, whether this cone will topple. [1]
\end{enumerate}
\hfill \mbox{\textit{OCR M2 Q1 [5]}}