| Exam Board | OCR |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2005 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Toppling and sliding of solids |
| Difficulty | Standard +0.3 This is a straightforward application of the toppling condition for a cone on an inclined plane. Part (i) requires knowing the center of mass is at h/4 from the base and applying tan(24°) = r/(h/4), then solving for r. Part (ii) is a simple comparison. Standard M2 mechanics with minimal problem-solving required. |
| Spec | 6.04e Rigid body equilibrium: coplanar forces |
| Answer | Marks | Guidance |
|---|---|---|
| (i) Use of \(h/4\) | B1 | |
| Com vert above lowest pt of contact | B1 | can be implied |
| \(r = 5 \times \tan 24°\) | M1 | |
| \(r = 2.2\) | A1 | 4 |
| (ii) No & valid reason (eg \(24° ÷ 26.6°\)) | B1 | 1 |
(i) Use of $h/4$ | B1 |
Com vert above lowest pt of contact | B1 | can be implied
$r = 5 \times \tan 24°$ | M1 |
$r = 2.2$ | A1 | 4 | 2.226
(ii) No & valid reason (eg $24° ÷ 26.6°$) | B1 | 1 | $\checkmark$ Yes if their $r \approx 2.5$ | 51\\
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A uniform solid cone has vertical height 20 cm and base radius $r \mathrm {~cm}$. 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 $24 ^ { \circ }$ (see diagram).\\
(i) Find $r$, correct to 1 decimal place.
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 $24 ^ { \circ }$.\\
(ii) State, with justification, whether this cone will topple.
\hfill \mbox{\textit{OCR M2 2005 Q1 [5]}}