A thin uniform rod mass `M` and length `L` is hinged at its upper end. And released from rest from a horizontal position. The tenstion at a point located at a distance `L//3` from the hinge point, when the rod become vertical will

Options

A. `22Mg//27`
B. `11Mg//13`
C. `6Mg//11`
D. `2Mg`

Explanation

To solve the problem, we will follow these steps:

### Step 1: Understand the System
The problem involves a thin uniform rod of mass \( M \) and length \( L \) that is hinged at one end and released from a horizontal position. When it becomes vertical, we need to find the tension at a point located at a distance \( \frac{L}{3} \) from the hinge.

### Step 2: Calculate the Loss in Potential Energy
When the rod is horizontal, its center of mass is at a height of \( \frac{L}{2} \) from the hinge. When it becomes vertical, the center of mass drops to a height of 0. The loss in potential energy (PE) can be calculated as:
\[
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