**Question:**

Two small balls $A$ and $B$, each of mass $m$, are joined rigidly by a light horizontal rod of length $L$. The rod is clamped at the centre in such a way that it can rotate freely about a vertical axis through its centre. The system is rotated with an angular speed $w$ about the axis. A particle $P$ of mass $m$ kept at rest sticks to the ball $A$ as the ball collides with it. Find the new angular speed of the rod.

**Solution:**

$\because^{\tau_{e x t}}=0$

$L_{i}=L_{f}$

${\left.\left[M^{\left(\frac{L}{2}\right)^{2}}+\mathrm{m}\left(\frac{L}{2}\right)^{2}\right] \omega=\left[3 m^{\frac{2}{2}}\right)^{2}\right] \omega^{\prime} }$

$\omega^{\prime}=3$

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