Find the length of seconds pendulum at a place where `g =4 pi^(2) m//s^(2)`.

Explanation

To find the length of a seconds pendulum at a place where \( g = 4\pi^2 \, \text{m/s}^2 \), we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Time Period of a Seconds Pendulum**:
A seconds pendulum is defined as a pendulum that has a time period of 2 seconds. Therefore, we have:
\[ T = 2 \, \text{seconds} \]

2. **Use the Formula for the Time Period of a Simple Pendulum**:
The time period \( T \) of a simple pendulum is given by the formula:
\[ T = 2\pi \sqrt{\frac{l}{g}} \]
where \( l \) is the length of the pendulum and \( g \) is the acceleration due to gravity.

3. **Substitute the Known Values**:
We know that \( T = 2 \) seconds and \( g = 4\pi^2 \, \text{m/s}^2 \). Substituting these values into the formula gives:
\[ 2 = 2\pi \sqrt{\frac{l}{4\pi^2}} \]

4. **Simplify the Equation**:
Divide both sides by \( 2 \):
\[ 1 = \pi \sqrt{\frac{l}{4\pi^2}} \]
Now, simplify the right side:
\[ 1 = \pi \cdot \frac{\sqrt{l}}{2\pi} = \frac{\sqrt{l}}{2} \]

5. **Isolate \( \sqrt{l} \)**:
Multiply both sides by 2:
\[ 2 = \sqrt{l} \]

6. **Square Both Sides**:
To find \( l \), square both sides:
\[ l = 2^2 = 4 \]

7. **Final Result**:
Therefore, the length of the seconds pendulum is:
\[ l = 4 \, \text{meters} \]