A rod of length L is hinged from one end. It is brought to a horizontal position and released. The angular velocity of the rod, when it is in vertical position, is

Options

A. `sqrt((2g)/L)`
B. `sqrt((3g)/(L))`
C. `sqrt(g/(2L))`
D. `sqrt(g/L)`

Explanation

To find the angular velocity of a rod of length \( L \) when it is in the vertical position after being released from the horizontal position, we can use the principle of conservation of energy. Here’s the step-by-step solution:

### Step 1: Understand the Initial and Final Positions
- The rod is initially in a horizontal position and is hinged at one end. When released, it rotates downwards to a vertical position.
- The center of mass of the rod is located at \( \frac{L}{2} \) from the hinge.

### Step 2: Calculate the Change in Potential Energy
- When the rod is horizontal, the height of the center of mass is \( \frac{L}{2} \).
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