When bullet meets pendulum

A pendulum consisting of a bob of mass \(M\) is suspended by a rigid rod of length \(L\). A bullet having the same mass as the bob and velocity \(v\) impacts the bob at an angle as shown in the figure and stays embedded in it. After the impact, the bob reaches a maximum angular displacement of \(\theta\). Find the value of initial velocity \(v\) of the bullet in \(\text{ms}^{-1}\).

Details and Assumptions:

  • Mass of the rod is negligible.

  • \(M = 39 \text{ kg}\).

  • \(\theta = 60^{\circ}\).

  • \(x = 30^{\circ}\).

  • \(L = 30 \text{ m}\).

  • Take \(g = 10 \text{ ms}^{-2}\).


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