What is the length of a simple pendulum which ticks second?

Options

A. 0.5 m
B. 1 m
C. 1.5 m
D. 2 m

Explanation

To find the length of a simple pendulum that ticks every second, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Time Period**: The problem states that the pendulum "ticks" every second, which means the time period (T) of the pendulum is 2 seconds.

2. **Use the Formula for Time Period**: 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 (approximately \( 10 \, \text{m/s}^2 \)).

3. **Square Both Sides**: To eliminate the square root, we square both sides of the equation:
\[ T^2 = (2\pi)^2 \frac{l}{g} \]

4. **Rearrange the Equation**: We can rearrange this equation to solve for \( l \):
\[ l = \frac{T^2 g}{(2\pi)^2} \]

5. **Substitute the Values**: We know \( T = 2 \, \text{s} \) and \( g \approx 10 \, \text{m/s}^2 \). Plugging these values into the equation:
\[ l = \frac{(2)^2 \cdot 10}{(2\pi)^2} \]

6. **Calculate the Length**:
- First, calculate \( (2)^2 = 4 \).
- Then calculate \( (2\pi)^2 = 4\pi^2 \).
- Substitute these into the equation:
\[ l = \frac{4 \cdot 10}{4\pi^2} = \frac{40}{4\pi^2} = \frac{10}{\pi^2} \]

7. **Approximate the Value**: Using \( \pi \approx 3.14 \):
\[ l \approx \frac{10}{(3.14)^2} \approx \frac{10}{9.8596} \approx 1.01 \, \text{m} \]
Rounding this, we find that the length of the pendulum is approximately \( 1 \, \text{m} \).

### Final Answer:
The length of the simple pendulum is **1 meter**.