The coefficient of superficial expansion of a solid is `2xx10//.^(@)C`. It's coefficient of linear expansion is

Options

A. `4xx10^(-5)//^(@)C`
B. `3xx10^(-5)//^(@)C`
C. `2xx10^(-5)//^(@)C`
D. `1xx10^(-5)//^(@)C`

Answer

To find the coefficient of linear expansion (α) from the coefficient of superficial expansion (β), we can use the relationship between these coefficients. The relationship is given by:

\[ \alpha = \frac{1}{2} \beta \]

### Step-by-Step Solution:

1. **Identify the given value of superficial expansion (β)**:
- We are given that the coefficient of superficial expansion (β) is \(2 \times 10^{-5} \, \text{°C}^{-1}\).

2. **Use the relationship between α and β**:
- According to the formula, the coefficient of linear expansion (α) is half of the coefficient of superficial expansion (β):
\[ \alpha = \frac{1}{2} \beta \]

3. **Substitute the value of β into the equation**:
- Now, substituting the value of β into the equation:
\[ \alpha = \frac{1}{2} \times (2 \times 10^{-5}) \]

4. **Calculate the value of α**:
- Performing the calculation:
\[ \alpha = \frac{2 \times 10^{-5}}{2} = 1 \times 10^{-5} \, \text{°C}^{-1} \]

5. **Final result**:
- Therefore, the coefficient of linear expansion (α) is:
\[ \alpha = 1 \times 10^{-5} \, \text{°C}^{-1} \]

### Answer:
The coefficient of linear expansion is \(1 \times 10^{-5} \, \text{°C}^{-1}\).

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