Question

theorem of perpendicular axes

Answer 1

Perpendicular Axis Theorem. For a planar object, the moment of inertia about an axis perpendicular to the plane is the sum of the moments of inertia of two perpendicular axes through the same point in the plane of the object.

Answer 2

The moment of inertia of a uniform plane lamina about an axis perpendicular to its plane equal to the sum of its moment of inertia about any two mutually perpendicular axis in its plane intersecting on first axis.

let ox nd oy is the plane of the lamina nd intersecting oz. Let us consider a partical P of mass m distance r from oz. So the moment of inertia IZ of whole lamina

IZ= sigma mr2
r2 = x2+ y2
r2= sigma m ( x2 + y2)
r2= sigma mx2 + sigma my2
IZ= IY+ IX
IZ= IX+ IY

I HOPE IT HELPS YOU