Question

A body of mass $M$ and radius $R$ is as shown in figure.
The body can be a ring, a disc, a hollow sphere or a solid sphere, $I_x,I_y,I_z$ are the moments of inertia about $x,y$ and $z$ axis respectively. Origin coincides with centre of mass of the body

Answer 1

$I_x=I_y=I_z$ is applicable for symmetrical body such as sphere.

$I_x=I_y+I_z$ (Perpendicular Theorem) is not possible for given figure,

$I_y=I_z+I_x$ not possible for sphere A/C to the given figure

$I_z=I_x+I_y$ This is for ring or disc from the figure we can find $I_z$ as $I_x$ and $I_y$ are mentioned.