A uniform rod OA of length l, resting on smooth surface is slightly distributed from its vertical position P is a point on the rod whose locus is a circle during the subsequent motion of the rod, then the distance OP is equal to 'l/4'. In the above question, the velocity of end O when end A hits the gournd is

Options

A. zero
B. along the horizontal
C. along the vertical
D. at some inclination of the ground `(ne90^(@))`

Explanation

To solve the problem step by step, we can follow this approach:

### Step 1: Understand the Setup
We have a uniform rod OA of length \( l \) resting on a smooth surface. The rod is slightly disturbed from its vertical position, and we know that point \( P \) on the rod moves in a circular path during the motion. We are given that the distance \( OP \) is equal to \( \frac{l}{4} \).

### Step 2: Identify the Motion of the Rod
When the rod is disturbed, it starts to rotate about its end \( O \) as it falls. The motion of the rod can be analyzed using rotational dynamics. The center of mass of the rod will experience a downward acceleration due to gravity.

...