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''`
`I_z + (ma^2)/(2)`
C. `I_x = I_y`
D. None of these

Answer

B

Explanation

(b) As `z` axis is parallel to `z'` axis and distance between them `= (a sqrt(2))/(2) = (a)/(sqrt(2))`
By the theorem of parallel axis,
`I'_z = I_z + m ((a)/(sqrt(2)))^2 = I_z + (ma^2)/(2)`
Hence, option (a) correct.
`z` and `z''` are not parallel axes. Hence, option (b) is incorrect.
By symmetry, `I_x = I_y`. Hence, option ( c) correct.