Question

An anisotropic solid metal cube has coefficients of linear expansion $5\times {10}^{-5}{/}^{\circ }\text{C}$ along the x - axis and $5\times {10}^{-6}{/}^{\circ }\text{C}$ along y - axis and z- axis. If the coefficient of volume expansion of the solid is $n\times {10}^{-6}{/}^{\circ }\text{C}$, then the value of $n$ is

Answer 1

For an anisotropic material, we know that
$\gamma ={\alpha }_x+{\alpha }_y+{\alpha }_z$
Here, from the data given in the question, ${\alpha }_y={\alpha }_z$
So,
$\gamma =2{\alpha }_y+{\alpha }_x$
$=10\times {10}^{-6}+5\times {10}^{-5}$
$=6\times {10}^{-5}{/}^{\circ }\text{C}$
$=60\times {10}^{-6}{/}^{\circ }\text{C}$
Thus, the value of $n$ is 60.