Question

A cuboid $ABCDEFGH$ is anisotropic with ${\alpha }_x=1\times {10}^{-5}{/}^{o}C,$ ${\alpha }_y=2\times {10}^{-5}{/}^{o}C,$ ${\alpha }_z=3\times {10}^{-5}{/}^{o}C.$ Coefficient of superficial expansion of faces can be

• A. ${\beta }_{ABCD}=5\times {10}^{-5}{/}^{\circ }C$
• B. ${\beta }_{BCGH}=4\times {10}^{-5}{/}^{\circ }C$
• C. ${\beta }_{CDEH}=3\times {10}^{-5}{/}^{\circ }C$
• D. ${\beta }_{EFGH}=2\times {10}^{-5}{/}^{\circ }C$

Answer 1

The correct option is C ${\beta }_{CDEH}=3\times {10}^{-5}{/}^{\circ }C$

$Given:$ ${\alpha }_x=1\times {10}^{-5}{/}^{o}C$ ; ${\alpha }_y=2\times {10}^{-5}{/}^{o}C$ ; ${\alpha }_z=3\times {10}^{-5}{/}^{o}C$

$Solution:$

Coefficient of superficial expansion of face $ABCD=a_x+a_z=4\times {10}^{-5}{/}^{\circ }C$

Coefficient of superficial expansion of face $BCGH={\alpha }_y+{\alpha }_z=5\times {10}^{-5}/{}^{\circ }C$

Coefficient of superficial expansion of face $CDEH=\alpha {}_x+\alpha {}_y=3\times {10}^{-5}/{}^{\circ }C$

Coefficient of superficial expansion of face $EFGH=\alpha {}_x+\alpha {}_z=4\times {10}^{-5}/{}^{\circ }C$

$So,the$ $correct$ $option:C$