| Exam Board | CAIE |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2015 |
| Session | June |
| Marks | 5 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Moments |
| Type | Lamina on surface with string or rod support |
| Difficulty | Standard +0.3 Part (i) requires recall of a standard formula (centre of mass of semicircle is 4r/3π from diameter). Part (ii) involves taking moments about B with the lamina vertical, requiring resolution of the applied force and use of the centre of mass location—straightforward application of equilibrium principles with no novel insight needed. Slightly easier than average due to the given force simplifying the problem. |
| Spec | 6.04c Composite bodies: centre of mass6.04e Rigid body equilibrium: coplanar forces |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(D = 2(0.8/2)\sin(\pi/2)/[3(\pi/2)]\) | M1 | |
| \(D = 0.17(0)\) m | A1 | [2 marks] |
| Answer | Marks | Guidance |
|---|---|---|
| Answer/Working | Mark | Guidance |
| \(0.17mg = 0.8(6\cos20)\) | M1, A1\(\checkmark\) | Moments about B; ft candidate value (0.17) |
| \(m = 2.66\) kg | A1 | [3 marks] Accept 2.65 |
## Question 1:
### Part (i):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $D = 2(0.8/2)\sin(\pi/2)/[3(\pi/2)]$ | M1 | |
| $D = 0.17(0)$ m | A1 | **[2 marks]** |
### Part (ii):
| Answer/Working | Mark | Guidance |
|---|---|---|
| $0.17mg = 0.8(6\cos20)$ | M1, A1$\checkmark$ | Moments about B; ft candidate value (0.17) |
| $m = 2.66$ kg | A1 | **[3 marks]** Accept 2.65 |
---1 A uniform semicircular lamina has diameter $A B$ of length 0.8 m .\\
(i) Find the distance of the centre of mass of the lamina from $A B$.
The lamina rests in a vertical plane, with the point $B$ of the lamina in contact with a rough horizontal surface and with $A$ vertically above $B$. Equilibrium is maintained by a force of magnitude 6 N in the plane of the lamina, applied to the lamina at $A$ and acting at an angle of $20 ^ { \circ }$ below the horizontal.\\
(ii) Calculate the mass of the lamina.
\hfill \mbox{\textit{CAIE M2 2015 Q1 [5]}}