A rod of mass \(m\) and length \(L\), pivoted at one of its ends, is hanging vertically. A bulle....

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A rod of mass \(m\) and length \(L\), pivoted at one of its ends, is hanging vertically. A bullet of the same mass moving at speed \(v\) strikes the rod horizontally at a distance \(x\) from its pivoted end and gets embedded in it. The combined system now rotates with angular speed \(\omega\) about the pivot. The maximum angular speed \(\omega_{m}\) is achieved for \(x=x_{M}\). Then
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