A non-isotropic solid metal cube has coefficient of linear expansion as `5 xx 10^(-5)//""^(@)C` along the x-axis and `5 xx 10^(-6)//""^(@)C` along y-axis and z-axis. If the coefficient of volumetric expansion of the solid is `n xx 10^(-6)//""^(@)C` then the value of n is....

Options

A. 5.5
B. 6.5
C. 60
D. 55

Answer

C

Explanation

Co-efficient of volume expansion = Co-efficient of linear expansion (in x-direction + in y-direction + in z-direction)
`=alpha_(x) + alpha_(y) + alpha_(z)`
`=5 xx 10^(-5) + 5 xx 10^(-6) +5 xx 10^(-6)`
`=50 xx 10^(-6) + 10 xx 10^(-6)`
`n xx 10^(-6) = 60 xx 10^(-6)`
`:. n= 60`