Parallel and Perpendicular Axis theorem is considered one the most difficult concept.
23 Questions around this concept.
For the given uniform square lamina ABCD, whose centre is O,

Consider a thin uniform square sheet made of a rigid material. If its side is 'a', mass m and moment of inertia I about one of its diagonals, then :
Consider a uniform square plate of side a and mass m. The moment of inertia of this plate about an axis perpendicular to its plane and passing through one of its corners is
The moment of inertia of a solid sphere, about an axis parallel to its diameter and at a distance of x from it, is 'I(x)'. Which one of the graphs represents the variation of I(x) with x correctly ?
Two identical spherical balls of mass M and radius R each are stuck on two ends of a rod of length 2R and mass M (see figure) The moment of inertia (MR2) of the system about the axis passing perpendicularly through the centre of the rod is :
From the theorem of the perpendicular axis. If the lamina is in the Y-Z plane
Parallel Axis Theorem-
$I_{b b^{\prime}}=I_{a a^{\prime}}+M h^2$

$b b^{\prime}$ is an axis parallel to $a a^{\prime} \& a a^{\prime}$ an axis passing through the center of mass.
Perpendicular Axis theorem-

$$
I_z=I_x+I_y
$$
(for a body in XY plane)
Where $I_z=$ moment of inertia about the $z$-axis
$I_x I_y$ : moment of inertia about the $\times \& y$-axis in the plane of the body respectively.
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