The time period of a seconds' pendulum :

Options

A. `2sec`
B. `(1)/(2)sec`
C. `1sec`
D. `1/4` sec

Explanation

To find the time period of a seconds' pendulum, we can follow these steps:

### Step 1: Understand the definition of a seconds' pendulum
A seconds' pendulum is defined as a pendulum that has a time period of 2 seconds. This means it takes 2 seconds to complete one full oscillation (back and forth).

### Step 2: Recall 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:
- \( T \) is the time period,
- \( L \) is the length of the pendulum,
- \( g \) is the acceleration due to gravity.

### Step 3: Assign values for a seconds' pendulum
For a seconds' pendulum:
- The length \( L \) is typically taken as 1 meter.
- The acceleration due to gravity \( g \) is approximately \( 10 \, \text{m/s}^2 \).

### Step 4: Substitute the values into the formula
Now, substituting the values into the formula:
\[ T = 2\pi \sqrt{\frac{1}{10}} \]

### Step 5: Calculate the square root
Calculating the square root:
\[ \sqrt{\frac{1}{10}} = \frac{1}{\sqrt{10}} \approx \frac{1}{3.16} \approx 0.316 \]

### Step 6: Calculate the time period
Now, substituting this back into the time period formula:
\[ T = 2\pi \times 0.316 \approx 2 \times 3.14 \times 0.316 \approx 1.993 \text{ seconds} \]

### Step 7: Round off the result
Rounding off gives us approximately \( 2 \) seconds.

### Conclusion
Thus, the time period of a seconds' pendulum is approximately \( 2 \) seconds.

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