The time period of a seconds pendululm is measured repeatedly for three times by two stop watches A, B . If the readings are as follows
`{:("S.NO.", A, B)(1, 2.01 "sec", 2.56 "sec"),(2, 2.10 "sec", 2.55 "sec"), (3, 1.98 "sec", 2.57 "sec"):}`

Options

A. A is more accurate but B is more precise
B. B is more accurate but A is more precise
C. A,B are equally precise
D. A, B are equally accurate.

Answer

To determine which stopwatch is more accurate and which is more precise, we need to analyze the provided readings from both stopwatches A and B.

### Step-by-Step Solution:

1. **List the Measurements:**
- Stopwatch A: 2.01 sec, 2.10 sec, 1.98 sec
- Stopwatch B: 2.56 sec, 2.55 sec, 2.57 sec

2. **Calculate the Mean for Stopwatch A:**
- Mean (A) = (2.01 + 2.10 + 1.98) / 3
- Mean (A) = (6.09) / 3
- Mean (A) = 2.03 sec

3. **Calculate the Mean for Stopwatch B:**
- Mean (B) = (2.56 + 2.55 + 2.57) / 3
- Mean (B) = (7.68) / 3
- Mean (B) = 2.56 sec

4. **Identify the True Value:**
- The true value for the time period of a second pendulum is 2.00 sec.

5. **Determine Accuracy:**
- Accuracy is determined by how close the mean value is to the true value.
- For Stopwatch A:
- Mean (A) = 2.03 sec, which is close to 2.00 sec.
- For Stopwatch B:
- Mean (B) = 2.56 sec, which is farther from 2.00 sec.
- Conclusion: Stopwatch A is more accurate.

6. **Determine Precision:**
- Precision is determined by how close the measurements are to each other.
- For Stopwatch A:
- Measurements: 2.01, 2.10, 1.98 (spread is larger)
- For Stopwatch B:
- Measurements: 2.56, 2.55, 2.57 (spread is smaller)
- Conclusion: Stopwatch B is more precise.

### Final Conclusion:
- Stopwatch A is more accurate.
- Stopwatch B is more precise.