# A non-isotropic solid metal cube has coefficients of linear expansion as:

Question:

A non-isotropic solid metal cube has coefficients of linear expansion as: $5 \times 10^{-5} /{ }^{\circ} \mathrm{C}$ along the $x$-axis and $5 \times 10^{-6} /{ }^{\circ} \mathrm{C}$ along the $y$ and the $z$-axis. If the coefficient of volume expansion of the solid is $\mathrm{C} \times 10^{-6 /{ }^{\circ} \mathrm{C} \text { then the value }}$ of $C$ is

Solution:

$(60.00) \quad$ Volume, $V=I b h$

$\therefore \gamma=\frac{\Delta V}{V}=\frac{\Delta \ell}{\ell}+\frac{\Delta b}{b}+\frac{\Delta h}{h}$

( $\gamma$ = coefficient of volume expansion)

$\Rightarrow \quad \gamma=5 \times 10^{-5}+5 \times 10^{-6}+5 \times 10^{-6}$

$=60 \times 10^{-6 /{ }^{\circ} \mathrm{C}}$

$\therefore \quad$ Value of $C=60.00$