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 $z^{\prime }$ is $I_z^{\prime }=I_z+\frac{m{a}^2}{2}$
• B. The moment of inertia of cube about $z"$ is $I_z^{\prime \prime }=I_z+\frac{m{a}^2}{2}$
• C. $I_x=I_y$
• D. None of these

Answer 1

Answer: (B)

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