Consider a material A has volume expansion coefficient \(\alpha_V = 3.9 \times 10^{-4}\)/°C. The linear expansion coefficient \(\alpha_l\) of the material A is:
DSSSB JE - 2023,
Answer: C
For an isotropic solid the volume expansion coefficient is three times the linear coefficient, \(\alpha_V = 3\alpha_l\), because the volume is the product of three lengths and each expands by the same fraction. Hence
\[ \begin{aligned} \alpha_l = \frac{3.9 \times 10^{-4}}{3} \\ &= 1.3 \times 10^{-4}\ /^{\circ}\text{C} \end{aligned} \]The option 3.9 x 10^-4 simply repeats the volume coefficient, 2.6 x 10^-4 corresponds to dividing by 1.5, and 10^-4 does not follow from any relation between the two coefficients.
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