The length of a simple pendulum is `39.2//pi^(2)` m. If `g=9.8 m//s^(2)` , the value of time period is

Options

A. 4 s
B. 8 s
C. 2 s
D. 3 s

Explanation

To find the time period of a simple pendulum, we can use the formula:

\[ T = 2\pi \sqrt{\frac{L}{g}} \]

Where:
- \( T \) is the time period,
- \( L \) is the length of the pendulum,
- \( g \) is the acceleration due to gravity.

### Step 1: Identify the given values
We are given:
- Length of the pendulum \( L = \frac{39.2}{\pi^2} \) m
- Acceleration due to gravity \( g = 9.8 \, \text{m/s}^2 \)

### Step 2: Substitute the values into the formula
Now, substituting the values of \( L \) and \( g \) into the time period formula:

\[ T = 2\pi \sqrt{\frac{\frac{39.2}{\pi^2}}{9.8}} \]

### Step 3: Simplify the expression
First, simplify the fraction inside the square root:

\[ T = 2\pi \sqrt{\frac{39.2}{9.8 \cdot \pi^2}} \]

Now, we can simplify \( \frac{39.2}{9.8} \):

\[ \frac{39.2}{9.8} = 4 \]

So, we can rewrite \( T \):

\[ T = 2\pi \sqrt{\frac{4}{\pi^2}} \]

### Step 4: Further simplification
Since \( \sqrt{\frac{4}{\pi^2}} = \frac{2}{\pi} \):

\[ T = 2\pi \cdot \frac{2}{\pi} \]

### Step 5: Calculate the final value
The \( \pi \) cancels out:

\[ T = 2 \cdot 2 = 4 \, \text{seconds} \]

Thus, the time period of the simple pendulum is:

\[ T = 4 \, \text{seconds} \]

### Conclusion
The correct option is **4 seconds**.

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