The coefficient of volumetric expansion of lamina is `5xx10^(-5)//""^(@)C`. Its coefficient of linear expansion will be:

Options

A. `1.6xx10^(-5)//""^(@)C`
B. `1.1xx10^(-5)//""^(@)C`
C. `2xx10^(-5)//""^(@)C`
D. `3xx10^(-5)//""^(@)C`

Explanation

To find the coefficient of linear expansion (α) from the given coefficient of volumetric expansion (γ), we can use the relationship between the two for isotropic materials. The relationship is given by:

\[ \gamma = 3\alpha \]

Where:
- \( \gamma \) is the coefficient of volumetric expansion.
- \( \alpha \) is the coefficient of linear expansion.

Given that the coefficient of volumetric expansion of the lamina is:

\[ \gamma = 5 \times 10^{-5} \, \text{°C}^{-1} \]

We can rearrange the formula to solve for \( \alpha \):

\[ \alpha = \frac{\gamma}{3} \]

Now, substituting the value of \( \gamma \):

\[ \alpha = \frac{5 \times 10^{-5}}{3} \]

Calculating this gives:

\[ \alpha = \frac{5}{3} \times 10^{-5} \, \text{°C}^{-1} \]

\[ \alpha \approx 1.6667 \times 10^{-5} \, \text{°C}^{-1} \]

Thus, the coefficient of linear expansion of the lamina is approximately:

\[ \alpha \approx 1.67 \times 10^{-5} \, \text{°C}^{-1} \]

### Final Answer:
The coefficient of linear expansion of the lamina is approximately \( 1.67 \times 10^{-5} \, \text{°C}^{-1} \).

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