Question

(A): the linear coefficients of expansion of a crystal along three perpendicular axes are $\alpha$,$\frac{-\alpha }{2}$, $\frac{\alpha }{5}$. its volume coefficient is $\frac{7\alpha }{10}$

(B): For an-isotropic solids

$r={\alpha }_x+{\alpha }_y+{\alpha }_z.$

• A. A and B are correct and B is correct explanation for A
• B. A and B are correct and B is not correct explanation for A
• C. A is true and B is false
• D. A and B both are wrong

Answer 1

The correct option is A A and B are correct and B is correct explanation for A

For anisotropic solids,

$V=xyz$

$\delta V=\frac{\partial V}{\partial x}\delta x+\frac{\partial V}{\partial y}\delta y+\frac{\partial V}{\partial z}\delta z$

$\delta V=yz\delta x+xz\delta y+xy\delta z$

$\frac{\delta V}{V}=\frac{\delta V}{xyz}=\frac{\delta x}{x}+\frac{\delta y}{y}+\frac{\delta z}{z}$

$\frac{\delta V}{V}=\alpha -\frac{\alpha }{2}+\frac{\alpha }{5}=\frac{7\alpha }{10}$

Hence answer is option A.