# Rod and particle

**Classical Mechanics**Level 5

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**

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