Suppose the amplitude of a simple pendulum having a bob of mass m is `theta_0`. Find the tension in the string when the bob is at its extreme position.

Explanation

To find the tension in the string of a simple pendulum when the bob is at its extreme position, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Setup**:
- We have a simple pendulum with a bob of mass \( m \).
- The amplitude of the pendulum is given as \( \theta_0 \). This means that at the extreme position, the pendulum is displaced by an angle \( \theta_0 \) from the vertical.

2. **Draw the Free Body Diagram**:
- At the extreme position, the forces acting on the bob are:
- The gravitational force \( mg \) acting downwards.
- The tension \( T \) in the string acting towards the pivot (along the string).

3. **Identify the Components of Forces**:
- At the extreme position, the angle between the string and the vertical is \( \theta_0 \).
- The component of the gravitational force along the direction of the string can be expressed as \( mg \cos \theta_0 \).

4. **Apply Newton's Second Law**:
- At the extreme position, the bob is momentarily at rest, which means its velocity \( v = 0 \).
- Therefore, the centripetal force required for circular motion is zero, and we can set up the equation:
\[ T - mg \cos \theta_0 = 0 \]
- This implies that the tension in the string must balance the component of the gravitational force acting along the string.

5. **Solve for Tension**:
- Rearranging the equation gives us:
\[ T = mg \cos \theta_0 \]
- This is the expression for the tension in the string when the bob is at its extreme position.

### Final Answer:
The tension in the string when the bob is at its extreme position is:
\[ T = mg \cos \theta_0 \]