With reference to Fig. of a cube of edge a and mass m, state whether the following are true or false. (O is the centre of the cube.)

Options

A. The moment of inertia of cube about `z^(')` is `I_(z)^(') = I_z + (ma^(2))/2`
B. The moment of inertia of cube about `z^('')` is `I_(z)^('')= I_z + (ma^(2))/2`
C. `I_x = I_y`
D. None of these

Answer

b

Explanation

As z axis is parallel to `z^(')` axis and distance between them `=(asqrt(2))/(2)= a/sqrt(2)`
By the theoremof parallel axes,
`I_(Z)^(')=I_(Z) + m(a/sqrt(2))^(2)= I_(Z)+(ma^(2))/(2)`
Hence, option (a) is correct.
z and `z^('')` are not parallel axes. Hence, option (b) is incorrect.
By symmetry, `I_(x)= I_(y)`, Hence option (c) is correct.