1 \includegraphics[max width=\textwidth, alt={}, center]{d3e9a568-a9ea-483e-8e65-90fdc4a69781-2_216_1205_253_470} A rigid body consists of two uniform circular discs, each of mass \(m\) and radius \(a\), the centres of which are rigidly attached to the ends \(A\) and \(B\) of a uniform rod of mass \(3 m\) and length \(10 a\). The discs and the rod are in the same plane and \(O\) is the point on the rod such that \(A O = 4 a\) (see diagram). Show that the moment of inertia of the body about an axis through \(O\) perpendicular to the plane of the discs is \(81 m a ^ { 2 }\).

## Question 1:

| Answer/Working | Mark | Guidance |
|---|---|---|
| $I_A = \frac{1}{2}ma^2 + m(4a)^2 = \frac{33}{2}ma^2$ | B1 | |
| $I_B = \frac{1}{2}ma^2 + m(6a)^2 = \frac{73}{2}ma^2$ | B1 | |
| $I_{rod} = \frac{1}{3}3m(5a)^2 + 3ma^2 = 28ma^2$ | B1 | |
| $I_{body} = I_A + I_B + I_{rod} = 81ma^2$ | M1 A1 | **A.G.** |

**Total: 5 marks**

---

1\\
\includegraphics[max width=\textwidth, alt={}, center]{d3e9a568-a9ea-483e-8e65-90fdc4a69781-2_216_1205_253_470}

A rigid body consists of two uniform circular discs, each of mass $m$ and radius $a$, the centres of which are rigidly attached to the ends $A$ and $B$ of a uniform rod of mass $3 m$ and length $10 a$. The discs and the rod are in the same plane and $O$ is the point on the rod such that $A O = 4 a$ (see diagram). Show that the moment of inertia of the body about an axis through $O$ perpendicular to the plane of the discs is $81 m a ^ { 2 }$.

\hfill \mbox{\textit{CAIE FP2 2012 Q1 [5]}}