**HC Verma’s Concepts of Physics – Chapter 10 – Question 15**

Find the moment of inertia of a uniform square plate of mass **m** and edge **a** about one of its diagonals.

The question was posted by Ankit

Solution:

Let the moment of inertia about the axis through the centre of the square plate perpendicular to the plane, assumed to be along Z axis, be I. Now the square plate will be in the XY plane. Let the X axis and Y axis be parallel to the edges and passing through the centre.

Then, we know that Ix = Iy = ma^{2}/12

Then, according to perpendicular axis theorem,

Iz = Ix + Iy = 2Ix=2ma^{2}/12=ma^{2}/6

Now, imagine that X and Y axes are along the diagonals. (The diagonals of a square are also mutually perpendicular.)

Again, according to perpendicular axis theorem, Iz = Ix + Iy = 2Ix

The MI about the diagonal about its diagonal, Ix = Iz/2 = **ma**^{2}/12

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