Question

An anisotropic material has coefficient of linear expansions as a, 2a and 3/2 a along x,y and z axis respectively. The coefficient of cubical expansion is

3a
9a
9/2a
3/2a

Please answer fast correctly​

Answer 1

Explanation:

An anisotropic material has a coefficient of linear expansions as a, 2a, and 3/2 an along x,y, and z-axis respectively. The coefficient of cubical expansion is  3a.

Answer 2

Given info : An anisotropic material has coefficient of linear expansions as a, 2a and 3/2 a along x,y and z axis respectively.

To find : The coefficient of cubical expansion is ..

solution : let material is heated to ∆T temperature,

so length of material along x - axis, x' = x(1 + a∆T)

length of material along y - axis, y' = y(1 + 2a∆T)

length of material along z - axis, z' = z(1 + 3a/2 ∆T)

now volume of material = x'y'z'

= x(1 + a∆T) × y(1 + 2a ∆T) × z(1 + 3a/2 ∆T)

= xyz (1 + a∆T)(1 + 2a∆T)(1 + 3a/2∆T)

= xyz [1 + (a + 2a + 3a/2)∆T]

[ neglecting product of two coefficients ]

= xyz (1 + 9a/2 ∆T)

hence it is clear that coefficient of cubical expansion is 9a/2.