The length of a rod is `(11.05+-0.05)cm`. What is the length of two such rods?

Options

A. `(22.1+-0.05)cm`
B. `(22.10+-0.05)cm`
C. `(22.1+-0.10)cm`
D. `(22.10+-0.10)cm`

Answer

To find the length of two rods, each with a length of \(11.05 \pm 0.05\) cm, we will follow these steps:

### Step 1: Identify the measured value and the error
The length of one rod is given as:
- Measured value (L) = \(11.05\) cm
- Error (ΔL) = \(0.05\) cm

### Step 2: Calculate the total length of two rods
Since the length of two rods is simply the sum of the lengths of each rod, we can write:
\[ L_{total} = L_1 + L_2 \]
Where \(L_1 = 11.05\) cm and \(L_2 = 11.05\) cm. Therefore:
\[ L_{total} = 11.05 + 11.05 = 22.10 \text{ cm} \]

### Step 3: Calculate the total error
When adding measurements, the errors also add up. Thus, the total error for the two rods is:
\[ \Delta L_{total} = \Delta L_1 + \Delta L_2 \]
Where \(\Delta L_1 = 0.05\) cm and \(\Delta L_2 = 0.05\) cm. Therefore:
\[ \Delta L_{total} = 0.05 + 0.05 = 0.10 \text{ cm} \]

### Step 4: Combine the results
Now, we can express the total length of the two rods along with the associated error:
\[ L_{total} = 22.10 \pm 0.10 \text{ cm} \]

### Final Answer
The length of two such rods is:
\[ 22.10 \pm 0.10 \text{ cm} \]

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