3. A uniform rod \(A B\), of mass \(m\) and length \(2 a\), is free to rotate about a fixed smooth axis which passes through \(A\) and is perpendicular to the rod. The rod has angular speed \(\omega\) when it strikes a particle \(P\) of mass \(m\) and adheres to it. Immediately before the rod strikes \(P , P\) is at rest and at a distance \(x\) from \(A\). Immediately after the rod strikes \(P\), the angular speed of the rod is \(\frac { 3 } { 4 } \omega\). Find \(x\) in terms of \(a\).
(5)

## Question 3:

| Working/Answer | Marks | Guidance |
|---|---|---|
| $\frac{4}{3}ma^2\omega = \left(\frac{4}{3}ma^2 + mx^2\right)\frac{3}{4}\omega$ | M1 A1 A1 | |
| $\Rightarrow x = \frac{2}{\sqrt{3}}a$ | DM1 A1 | **(5)** |

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3. A uniform rod $A B$, of mass $m$ and length $2 a$, is free to rotate about a fixed smooth axis which passes through $A$ and is perpendicular to the rod. The rod has angular speed $\omega$ when it strikes a particle $P$ of mass $m$ and adheres to it. Immediately before the rod strikes $P , P$ is at rest and at a distance $x$ from $A$. Immediately after the rod strikes $P$, the angular speed of the rod is $\frac { 3 } { 4 } \omega$.

Find $x$ in terms of $a$.\\
(5)\\

\hfill \mbox{\textit{Edexcel M5 2007 Q3 [5]}}