Potential energy of the bob is maximum

Options

A. at the mean position
B. at the extreme positions
C. between the mean position and extreme positions
D. none of these

Answer

To determine when the potential energy of the bob in a simple pendulum is maximum, we can analyze the motion of the pendulum step by step.

### Step-by-Step Solution:

1. **Understanding the Pendulum Setup**:
- A simple pendulum consists of a mass (bob) attached to a string fixed at one end. The bob swings back and forth under the influence of gravity.

2. **Identifying Key Positions**:
- The **mean position** (or equilibrium position) is where the bob hangs straight down, and the net force acting on it is zero.
- The **extreme positions** are the highest points the bob reaches on either side of the mean position during its swing.

3. **Potential Energy and Height**:
- The potential energy (PE) of the bob is given by the formula:
\[ PE = mgh \]
where \( m \) is the mass of the bob, \( g \) is the acceleration due to gravity, and \( h \) is the height of the bob above a reference point (usually taken as the mean position).

4. **Analyzing Energy at Different Positions**:
- At the mean position, the height \( h \) is zero, so the potential energy is also zero:
\[ PE_{\text{mean}} = mg \cdot 0 = 0 \]
- As the bob swings up towards the extreme position, its height \( h \) increases, and consequently, its potential energy increases.

5. **Maximum Potential Energy**:
- At the extreme position, the bob reaches its maximum height \( h \). Therefore, the potential energy is maximum at this point:
\[ PE_{\text{extreme}} = mg \cdot h_{\text{max}} \]
- Since \( h \) is maximum at the extreme position, the potential energy is also maximum here.

6. **Conclusion**:
- The potential energy of the bob is maximum at the extreme positions of its swing.

### Answer:
The potential energy of the bob is maximum at the extreme position (Option 2).