In order to measure period of a simple pendulum using a stop clock a student repeated the experiment for 10 times and noted down the time period for each experiment as 5.1, 5.0, 4.9, 5.1, 5.0, 4.9, 5.1, 5.0, 4.9 ,5.0s
the correct way of expressing the result for the period is

Options

A. 4.99 s
B. 5.0 s
C. 5.00 s
D. 4.9 s

Answer

To determine the correct way of expressing the result for the period of a simple pendulum based on the repeated measurements, we can follow these steps:

### Step 1: List the Recorded Time Periods
The student recorded the time periods for 10 experiments as follows:
- 5.1 s
- 5.0 s
- 4.9 s
- 5.1 s
- 5.0 s
- 4.9 s
- 5.1 s
- 5.0 s
- 4.9 s
- 5.0 s

### Step 2: Calculate the Average Time Period
To find the average time period, we sum all the recorded time periods and then divide by the number of measurements (10).

\[ \text{Average} = \frac{(5.1 + 5.0 + 4.9 + 5.1 + 5.0 + 4.9 + 5.1 + 5.0 + 4.9 + 5.0)}{10} \]

Calculating the sum:
\[ 5.1 + 5.0 + 4.9 + 5.1 + 5.0 + 4.9 + 5.1 + 5.0 + 4.9 + 5.0 = 50.0 \]

Now, divide by 10:
\[ \text{Average} = \frac{50.0}{10} = 5.0 \text{ s} \]

### Step 3: Determine the Significant Figures
The recorded time periods have two significant figures (e.g., 5.1, 5.0, 4.9). Therefore, the average result should also be expressed with the same number of significant figures.

### Step 4: Express the Result
Since the average time period is 5.0 s, we can express it as:
\[ \text{Result} = 5.0 \text{ s} \]

This maintains the two significant figures consistent with the measurements taken.

### Final Answer
The correct way of expressing the result for the period is:
\[ \text{Period} = 5.0 \text{ s} \]

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