# The sum of the moment of inertias of two mutually perpendicular arbitrary axis is

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## Options:

1. varies directly as the square of smaller value

2. zero

3. always constant

4. different for different orientations

### Correct Answer: Option 3 (Solution Below)

This question was previously asked in

TN TRB Civil 2012 Paper

## Solution:

Perpendicular axis theorem: The moment of inertia of a plane lamina about an axis that is perpendicular to the plane of the lamina is equal to the sum of the moments of inertia of the lamina about the two-axis at perpendicular to each other, in its plane intersecting each other at the point.

Iz = Ixx + Iyy = I’x + I’y

Where Iis the moment of inertia about Z-axis, IX is the moment of inertia about X-axis and IY is the moment of inertia about Y-axis

∴ The sum of the moment of inertias of two mutually perpendicular arbitrary axis is always constant.
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