If the length of rod A is 3.25 `pm` 0.01 cm and that of B is 4.19 `pm` 0.01 cm then the rod B is longer than rod A by

Options

A. `0.94+-0.00cm`
B. `0.94+-0.01cm`
C. `0.94+-0.02cm`
D. `0.94+-0.005cm`

Answer

To solve the problem, we need to find the difference in lengths between rod B and rod A, taking into account the uncertainties in their measurements.

### Step-by-Step Solution:

1. **Identify the lengths and uncertainties of the rods:**
- Length of rod A (L_A) = 3.25 cm with an uncertainty of ±0.01 cm.
- Length of rod B (L_B) = 4.19 cm with an uncertainty of ±0.01 cm.

2. **Calculate the difference in lengths:**
- The difference in lengths (X) can be calculated as:
\[ X = L_B - L_A = (4.19 \, \text{cm}) - (3.25 \, \text{cm}) \]

3. **Perform the subtraction:**
- Calculate:
\[ X = 4.19 - 3.25 = 0.94 \, \text{cm} \]

4. **Calculate the total uncertainty:**
- The uncertainty in the difference is the sum of the uncertainties of both measurements:
\[ \text{Total uncertainty} = \text{Uncertainty of } L_B + \text{Uncertainty of } L_A = 0.01 \, \text{cm} + 0.01 \, \text{cm} = 0.02 \, \text{cm} \]

5. **Combine the results:**
- Therefore, the final result for the difference in lengths, including the uncertainty, is:
\[ X = 0.94 \pm 0.02 \, \text{cm} \]

### Final Answer:
Rod B is longer than rod A by \(0.94 \pm 0.02 \, \text{cm}\).

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