Question

A two dimensional lamina of arbitrary shape is placed in $x-y$ plane as shown in the figure. $\text{MOI}$ of lamina about $x$ and $y$ axes are $I_x=6{\text{kg-m}}^2$ and $I_y=4{\text{kg-m}}^2$ respectively. If point of intersection $\left(O\right)$ of the axes does not lies on lamina, then the $\text{MOI}$ of lamina about $z$ axis i.e. $\left(I_z\right)$ will be

• A. $6{\text{kg-m}}^2$
• B. $4{\text{kg-m}}^2$
• C. $8{\text{kg-m}}^2$
• D. $10{\text{kg-m}}^2$

Answer 1

The correct option is D $10{\text{kg-m}}^2$


Given, $I_x=6{\text{kg-m}}^2$ and $I_y=4{\text{kg-m}}^2$
As we know,
For using Perpendicular axis theorem, point of intersection of the three axis need not be $\text{COM}$, it can be any point in the plane of body which lies on the body or even outside it.

$\therefore$ Using Perpendicular axis theorem we get
$I_z=I_x+I_y=(6+4){\text{kg-m}}^2=10{\text{kg-m}}^2$