A uniform rod OA of length l resting on smooth surface slightly disturbed from its vertical position . P is a ipoint on the rod whose locus is a circle during the subsequent motion of the rod. the OP distance is l/4 . In the above question, the velocity of end A at the instant it hits the ground is

Options

A. `sqrt(3gl)`
B. `sqrt(12gl)`
C. `sqrt(6gl)`
D. none of these

Explanation

To solve the problem, we need to find the velocity of the end A of the rod at the instant it hits the ground after being slightly disturbed from the vertical position.

### Step-by-Step Solution:

1. **Understand the System**:
- We have a uniform rod OA of length \( l \) resting on a smooth surface.
- The rod is slightly disturbed from its vertical position, and point P on the rod has a distance \( OP = \frac{l}{4} \).
- The rod will rotate about point O when it falls.
...