An iron bar of length 10 m is heated from `0^@C " to " 100^@C`. If the coefficient of linear thermal expansion of iron is `10xx10^(-6) .^@C^(-1)` , then increase in the length of bar (in cm ) is

Options

A. (a)0.5 cm
B. (b)1.0 cm
C. (c)1.5 cm
D. (d)2.0 cm

Answer

To solve the problem of finding the increase in length of an iron bar when heated, we can follow these steps:

### Step 1: Understand the formula for linear thermal expansion
The formula for the change in length (ΔL) due to thermal expansion is given by:
\[ \Delta L = \alpha \cdot L \cdot \Delta T \]
where:
- ΔL is the change in length,
- α is the coefficient of linear thermal expansion,
- L is the original length of the bar,
- ΔT is the change in temperature.

### Step 2: Identify the given values
From the problem statement, we have:
- Original length (L) = 10 m
- Coefficient of linear thermal expansion (α) = \(10 \times 10^{-6} \, ^\circ C^{-1}\)
- Initial temperature = \(0 \, ^\circ C\)
- Final temperature = \(100 \, ^\circ C\)

### Step 3: Calculate the change in temperature (ΔT)
\[ \Delta T = \text{Final temperature} - \text{Initial temperature} = 100 \, ^\circ C - 0 \, ^\circ C = 100 \, ^\circ C \]

### Step 4: Substitute the values into the formula
Now we can substitute the values into the formula:
\[ \Delta L = (10 \times 10^{-6}) \cdot (10) \cdot (100) \]

### Step 5: Perform the calculation
Calculating the above expression:
\[ \Delta L = 10 \times 10^{-6} \times 10 \times 100 = 10 \times 10^{-6} \times 1000 = 10 \times 10^{-3} = 10^{-2} \, \text{m} \]

### Step 6: Convert the change in length from meters to centimeters
Since 1 m = 100 cm, we convert ΔL:
\[ \Delta L = 10^{-2} \, \text{m} = 10^{-2} \times 100 \, \text{cm} = 1 \, \text{cm} \]

### Final Answer
The increase in the length of the bar is **1 cm**.

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