Question

A two dimensional object lies in $x-z$ plane having moment of inertia $I_X=M{R}^2$ and $I_Y=4M{R}^2$. Then, the moment of inertia of object along $z-$axis is

• A. $I_Z=3M{R}^2$
• B. $I_Z=5M{R}^2$
• C. $I_Z=\sqrt{17}M{R}^2$
• D. $I_Z=\sqrt{10}M{R}^2$

Answer 1

The correct option is A $I_Z=3M{R}^2$

Given, $I_X=M{R}^2$ and $I_Y=4M{R}^2$
We know from definition of Perpendicuar axis theorem for an object lies in $x-z$ plane
$I_Y=I_X+I_Z$
$\Rightarrow 4M{R}^2=M{R}^2+I_Z$
$\Rightarrow I_Z=3M{R}^2$