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. 0.5 cm
B. 1.0 cm
C. 1.5 cm
D. 2.0 cm

Answer

To find the increase in length of the iron bar when heated, we can use the formula for linear thermal expansion:

\[ \Delta L = \alpha \cdot L_0 \cdot \Delta T \]

Where:
- \(\Delta L\) = change in length
- \(\alpha\) = coefficient of linear thermal expansion
- \(L_0\) = original length of the bar
- \(\Delta T\) = change in temperature

### Step 1: Identify the given values
- Original length of the bar, \(L_0 = 10 \, \text{m}\)
- Coefficient of linear thermal expansion, \(\alpha = 10 \times 10^{-6} \, \text{°C}^{-1}\)
- Initial temperature, \(T_i = 0 \, \text{°C}\)
- Final temperature, \(T_f = 100 \, \text{°C}\)

### Step 2: Calculate the change in temperature
\[ \Delta T = T_f - T_i = 100 \, \text{°C} - 0 \, \text{°C} = 100 \, \text{°C} \]

### Step 3: Substitute the values into the formula
\[ \Delta L = (10 \times 10^{-6}) \cdot (10) \cdot (100) \]

### Step 4: Perform the calculations
\[ \Delta L = 10 \times 10^{-6} \cdot 10 \cdot 100 = 10 \times 10^{-6} \cdot 1000 = 10 \times 10^{-3} \, \text{m} \]

### Step 5: Convert meters to centimeters
Since \(1 \, \text{m} = 100 \, \text{cm}\):
\[ \Delta L = 10 \times 10^{-3} \, \text{m} = 10 \, \text{cm} \]

### Final Answer
The increase in the length of the iron bar is \(1 \, \text{cm}\).

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