# 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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