A uniform bar of length 12 cm and mass $20m$ lies on a smooth horizontal table. Two point masses m a

Question

A uniform bar of length 12 cm and mass $20m$ lies on a smooth horizontal table. Two point masses m and $2m$ are moving in opposite directions with same speed of v and in the same plane as the bar, as shown in figure. These masses strike the bar simultaneously and get stuck to it. After collision the entire system is rotating with angular frequency $\omega$. The ratio of v and $\omega$ is :

Accepted Answer

Using angular momentum conservation about COM of rod :

$$L_{i} = L_{f}$$

$$\begin{matrix} m \times V \times 4 & \ + 2\text{ }m \times V \times 2 = \left( \frac{20\text{ }m(12)^{2}}{12} + m \times 4^{2} + 2\text{ }m \times 2^{2} \right)\omega \\ 8mV & \ = (240\text{ }m + 24\text{ }m)\omega \\ 8\text{ }V & \ = 264\omega \\ \frac{\text{ }V}{\omega} & \ = 33 \end{matrix}$$

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