A rod of length L and mass m is kept vertically on the ground. Its potential energy is :

Options

A. (a)mgL
B. (b)`mg.(L)/(2)`
C. (c)`mg.(L)/(3)`
D. (d)`mg.(L)/(4)`

Answer

To find the potential energy of a rod of length L and mass m kept vertically on the ground, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Potential Energy**:
The potential energy (PE) of an object is given by the formula:
\[ PE = mgh \]
where \(m\) is the mass of the object, \(g\) is the acceleration due to gravity, and \(h\) is the height of the center of mass above a reference point (in this case, the ground).

2. **Identify the Height of the Center of Mass**:
For a uniform rod of length \(L\), the center of mass is located at the midpoint of the rod. Therefore, the height \(h\) of the center of mass above the ground is:
\[ h = \frac{L}{2} \]

3. **Substitute Values into the Potential Energy Formula**:
Now, substituting the values of \(m\), \(g\), and \(h\) into the potential energy formula:
\[ PE = mg \left(\frac{L}{2}\right) \]

4. **Simplify the Expression**:
This simplifies to:
\[ PE = \frac{mgL}{2} \]

5. **Conclusion**:
Thus, the potential energy of the rod is:
\[ PE = \frac{mgL}{2} \]

### Final Answer:
The potential energy of the rod is \(\frac{mgL}{2}\).