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  4. A non-isotropic solid metal cube has coefficients of linear expansion as: 5× 10- 5/° C along the X-axis and 5× 10- 6/° C along the y and the z -axis. If the coefficient of volume expansion of the solid is C× 10- 6/° C then the value C is

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

NTA AbhyasNTA Abhyas 2022

Solution:

$V=2\alpha _{2}+\alpha _{1}=10\times 10^{- 6}+5\times 10^{- 5}=60\times 10^{- 6}/{}^{^\circ }C$