A bob of simple pendulum is suspended by a metallic wire. If `alpha` is the coefficient of linear expansion and `d theta` is t he change in temperature then prove that percentage change in time period is `50 alpha d theta`.

Explanation

To solve the problem, we need to prove that the percentage change in the time period of a simple pendulum, when the temperature changes, is given by \(50 \alpha d\theta\), where \(\alpha\) is the coefficient of linear expansion and \(d\theta\) is the change in temperature.

### Step-by-step Solution:

1. **Understand the Time Period Formula**:
The time period \(T\) of a simple pendulum is given by the formula:
\[
T = 2\pi \sqrt{\frac{L}{g}}
...