The time period of a simple pendulum of length 9.8 m is

Options

A. 0.159 s
B. 3.14 s
C. 6.5 s
D. 6.28 s

Explanation

To find the time period of a simple pendulum of length 9.8 m, we can use the formula for the time period \( T \) of a simple pendulum:

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

where:
- \( T \) is the time period,
- \( L \) is the length of the pendulum,
- \( g \) is the acceleration due to gravity (approximately \( 9.8 \, \text{m/s}^2 \)).

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

### Step 2: Substitute the values into the formula
Now, we can substitute the values into the formula:

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

### Step 3: Simplify the fraction
The fraction simplifies as follows:

\[ \frac{9.8}{9.8} = 1 \]

### Step 4: Calculate the square root
Taking the square root of 1 gives:

\[ \sqrt{1} = 1 \]

### Step 5: Calculate the time period
Now, substituting back into the equation for \( T \):

\[ T = 2\pi \times 1 = 2\pi \]

### Step 6: Calculate \( 2\pi \)
Using the approximate value of \( \pi \approx 3.14 \):

\[ T = 2 \times 3.14 = 6.28 \, \text{seconds} \]

### Final Answer
Thus, the time period of the simple pendulum of length 9.8 m is:

\[ \boxed{6.28 \, \text{seconds}} \]