What is the period of a simple pendulum whose length is 50 cm?

Explanation

To find the period of a simple pendulum with a given length, we can follow these steps:

### Step 1: Identify the length of the pendulum
The length of the pendulum (L) is given as 50 cm. We need to convert this into meters for consistency with the standard units used in the formula.

- **Conversion**:
\[ L = 50 \, \text{cm} = 0.5 \, \text{m} \]

### Step 2: Recall the formula for the period of a simple pendulum
The formula for the period (T) of a simple pendulum is given by:
\[ T = 2\pi \sqrt{\frac{L}{g}} \]
where:
- \( T \) is the period,
- \( L \) is the length of the pendulum,
- \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \), but we can use \( 10 \, \text{m/s}^2 \) for simplicity in calculations).

### Step 3: Substitute the values into the formula
Now, we substitute the values of \( L \) and \( g \) into the formula:
\[ T = 2\pi \sqrt{\frac{0.5}{10}} \]

### Step 4: Calculate the value inside the square root
First, calculate \( \frac{0.5}{10} \):
\[ \frac{0.5}{10} = 0.05 \]

### Step 5: Calculate the square root
Now, find the square root of \( 0.05 \):
\[ \sqrt{0.05} \approx 0.2236 \]

### Step 6: Multiply by \( 2\pi \)
Now, calculate \( T \):
\[ T = 2\pi \times 0.2236 \approx 1.4 \, \text{seconds} \]

### Conclusion
The period of the simple pendulum whose length is 50 cm is approximately \( 1.4 \, \text{seconds} \).

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