Rod and particle

Consider a rod of mass \(M \) and length \(L\) is free to rotate about an horizontal axis O passing through its center. A particle of mass m falls from point P which is at a height h from Q and collides elastically with rod at a distance \(\frac L4\) form O. If the rod makes an angle \(\alpha\) with horizontal before collision. Then find the angular velocity of rod just after collision.

Details And Assumptions

  1. The Rod is at rest before collision
  2. M = 2.5 kg
  3. L = 4 m
  4. m = 2 kg
  5. h = 5 m
  6. \(\alpha = {37}^{\circ}\)
  7. Take \(g= 10 m/s^2\)

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