Kinetic energy of the bob of a simple pendulum is maximum

Options

A. at the mean position
B. at the extreme left position
C. at the extreme right position
D. none of these

Answer

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

### Step-by-Step Solution:

1. **Understanding the Pendulum's Motion**:
- A simple pendulum consists of a mass (bob) attached to a string that swings back and forth. The pendulum oscillates around a central point known as the mean position.

2. **Identifying Key Positions**:
- **Mean Position**: This is the lowest point in the swing where the bob hangs vertically down. Here, the forces acting on the bob are balanced (tension equals weight).
- **Extreme Positions**: These are the highest points on either side of the mean position, where the bob momentarily comes to rest before reversing direction.

3. **Velocity at Different Positions**:
- At the **mean position**, the bob is moving at its maximum speed because all the potential energy has been converted into kinetic energy.
- At the **extreme positions** (both left and right), the velocity of the bob is zero because it momentarily stops before changing direction.

4. **Kinetic Energy Calculation**:
- Kinetic energy (KE) is given by the formula:
\[ KE = \frac{1}{2} mv^2 \]
where \( m \) is the mass of the bob and \( v \) is its velocity.
- Since the velocity at the extreme positions is zero, the kinetic energy at these points is:
\[ KE = \frac{1}{2} m(0)^2 = 0 \]
- At the mean position, since the velocity is maximum, the kinetic energy is at its highest value.

5. **Conclusion**:
- Therefore, the kinetic energy of the bob of a simple pendulum is maximum at the **mean position**.

### Final Answer:
The kinetic energy of the bob of a simple pendulum is maximum at the mean position.

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