A uniform thin rod of mass `m` and length `l` is standing on a smooth horizontal suface. A slight disturbance causes the lower end to slip on the smooth surface and the rod starts falling. Find the velocity of centre of mass of the rod at the instant when it makes an angle `theta` with horizontal.

Explanation

To solve the problem, we will use the principle of conservation of energy. We will analyze the potential energy lost by the center of mass of the rod as it falls and equate it to the kinetic energy gained by the rod.

### Step-by-Step Solution:

1. **Understanding the Initial and Final Positions:**
- Initially, the rod is vertical, and its center of mass is at a height of \( \frac{l}{2} \) from the ground.
- When the rod makes an angle \( \theta \) with the horizontal, the height of the center of mass from the ground is \( h = \frac{l}{2} - \frac{l}{2} \sin \theta = \frac{l}{2} (1 - \sin \theta) \).

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