| Exam Board | Edexcel |
|---|---|
| Module | M3 (Mechanics 3) |
| Year | 2017 |
| Session | June |
| Marks | 9 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Centre of Mass 1 |
| Type | Conical or hemispherical shell composite |
| Difficulty | Standard +0.3 This is a standard M3 centre of mass question involving composite bodies with known formulae. Part (a) requires applying the hemispherical shell centre of mass formula (a/2 from centre) and taking moments - straightforward bookwork. Part (b) uses the standard toppling condition (vertical through COM passes through edge). While it requires careful setup and algebra, it follows a well-practiced method with no novel insight needed. Slightly easier than average due to the routine nature of both parts. |
| Spec | 6.04b Find centre of mass: using symmetry6.04c Composite bodies: centre of mass6.04e Rigid body equilibrium: coplanar forces |
4.
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A thin uniform right hollow cylinder, of radius $a$ and height $4 a$, has a base but no top. A thin uniform hemispherical shell, also of radius $a$, is made of the same material as the cylinder. The hemispherical shell is attached to the open end of the cylinder forming a container $C$. The open circular rim of the cylinder coincides with the rim of the hemispherical shell. The centre of the base of $C$ is $O$, as shown in Figure 3.
\begin{enumerate}[label=(\alph*)]
\item Find the distance from $O$ to the centre of mass of $C$.
The container is placed with its circular base on a plane which is inclined at $\theta ^ { \circ }$ to the horizontal. The plane is sufficiently rough to prevent $C$ from sliding. The container is on the point of toppling.
\item Find the value of $\theta$.
\end{enumerate}
\hfill \mbox{\textit{Edexcel M3 2017 Q4 [9]}}