The length of one rod `l_(1)=3.323cm` and the other is `l_(2)=3.321cm` both rods were measured with one measuring instrument with least count 0.001 cm Then`(l_(1)-l_(2))` is

Options

A. `(0,002 pm 0.001)cm`
B. `(0.002 pm 0.000)cm`
C. `(0.002 pm 0.002)cm`
D. None of these

Explanation

To solve the problem of finding \( l_1 - l_2 \) given the lengths of two rods and their uncertainties, we will follow these steps:

1. **Identify the lengths and uncertainties**:
- The length of the first rod \( l_1 = 3.323 \, \text{cm} \) with an uncertainty of \( \Delta l_1 = 0.001 \, \text{cm} \).
- The length of the second rod \( l_2 = 3.321 \, \text{cm} \) with an uncertainty of \( \Delta l_2 = 0.001 \, \text{cm} \).

2. **Calculate the difference in lengths**:
\[ l_1 - l_2 = 3.323 \, \text{cm} - 3.321 \, \text{cm} = 0.002 \, \text{cm} \]

3. **Determine the uncertainty in the difference**:
- When subtracting two measurements, the uncertainties add up. Therefore, the total uncertainty \( \Delta (l_1 - l_2) \) is given by:
\[ \Delta (l_1 - l_2) = \Delta l_1 + \Delta l_2 = 0.001 \, \text{cm} + 0.001 \, \text{cm} = 0.002 \, \text{cm} \]

4. **Combine the results**:
- The result for \( l_1 - l_2 \) with its uncertainty is:
\[ l_1 - l_2 = 0.002 \, \text{cm} \pm 0.002 \, \text{cm} \]

5. **Final result**:
- Thus, the final answer is:
\[ l_1 - l_2 = 0.002 \, \text{cm} \pm 0.002 \, \text{cm} \]