The period of oscillation of a simple pendulum in the experiment is recorded as `2.63 s , 2.56 s , 2.42 s , 2.71 s , and 2.80 s`. Find the average absolute error.

Options

A. 0.11 s
B. 0.12 s
C. 0.13 s
D. 0.14 s

Explanation

To find the average absolute error of the period of oscillation of a simple pendulum based on the given measurements, we can follow these steps:

### Step 1: Calculate the Average Time Period
First, we need to find the average time period (T_avg) from the given measurements.

Given measurements:
- T1 = 2.63 s
- T2 = 2.56 s
- T3 = 2.42 s
- T4 = 2.71 s
- T5 = 2.80 s

The average time period is calculated as follows:
\[ T_{avg} = \frac{T_1 + T_2 + T_3 + T_4 + T_5}{5} \]
Substituting the values:
\[ T_{avg} = \frac{2.63 + 2.56 + 2.42 + 2.71 + 2.80}{5} = \frac{13.12}{5} = 2.62 \text{ s} \]

### Step 2: Calculate the Absolute Errors
Next, we calculate the absolute error for each measurement using the formula:
\[ \Delta T_i = |T_i - T_{avg}| \]
Where \(T_i\) is each individual measurement.

Calculating each absolute error:
1. For T1:
\[ \Delta T_1 = |2.63 - 2.62| = 0.01 \text{ s} \]
2. For T2:
\[ \Delta T_2 = |2.56 - 2.62| = 0.06 \text{ s} \]
3. For T3:
\[ \Delta T_3 = |2.42 - 2.62| = 0.20 \text{ s} \]
4. For T4:
\[ \Delta T_4 = |2.71 - 2.62| = 0.09 \text{ s} \]
5. For T5:
\[ \Delta T_5 = |2.80 - 2.62| = 0.18 \text{ s} \]

### Step 3: Calculate the Average Absolute Error
Now, we find the average of these absolute errors:
\[ \text{Average Absolute Error} = \frac{\Delta T_1 + \Delta T_2 + \Delta T_3 + \Delta T_4 + \Delta T_5}{5} \]
Substituting the values:
\[ \text{Average Absolute Error} = \frac{0.01 + 0.06 + 0.20 + 0.09 + 0.18}{5} = \frac{0.54}{5} = 0.108 \text{ s} \approx 0.11 \text{ s} \]

### Final Answer
The average absolute error is approximately **0.11 seconds**.

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