A uniform slender rod of mass `m` and length `L` is released from rest, with its lower end touching a frictionaless horizontal floor. At the initial moment, the rod is inclined at an angle `theta=30^(@)` with the vertical. Thent he value of normal reaction from the from the floor just after release will be

Options

A. `4mg//7`
B. `5mg//9`
C. `2mg//5`
D. None of these

Explanation

To solve the problem of finding the normal reaction from the floor just after the release of a uniform slender rod inclined at an angle of \( \theta = 30^\circ \) with the vertical, we can follow these steps:

### Step 1: Draw the Diagram
We start by visualizing the problem. Draw a vertical line representing the vertical direction. Then, draw the rod inclined at \( 30^\circ \) to the vertical. Label the lower end of the rod as point O (the point touching the floor) and the upper end as point P. The center of mass (C) of the rod is located at its midpoint.

### Step 2: Identify Forces Acting on the Rod
The forces acting on the rod are:
- The weight of the rod \( mg \) acting downward through the center of mass.
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