Question

With reference to figure of a cube of edge a and mass m, which of the following is the incorrect statement?
($O$ is the centre of the cube)

• A. The moment of inertia of cube about $z'$ is $I'_z = I_z + \frac{ma^2} {2}$
• B. The moment of inertia of cube about $z"$ is $I''_z = I_z + \frac{ma^2} {2}$
• C. $I_x = I_y$
• D. None of these

Answer 1

Answer: (B)

As $z$ axis is parallel to $z'$ axis and distance between them
$ = \frac{a\sqrt 2}{2} = \frac{a}{\sqrt 2}$
By the theorem of parallel axes,
$I'_z = I_z + m (\frac{a}{\sqrt 2})^2 = I_z + \frac{ma^2}{2}$
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.