Question

A lamina lies in $y-z$ plane having moment of inertia about $x$ axis $I_x=6M{R}^2$ and moment of inertia about $y-$ axis $I_y=3M{R}^2$. Then, the moment of inertia of the lamina about $z$ axis is

• A. $9M{R}^2$
• B. $3M{R}^2$
• C. $\sqrt{27}M{R}^2$
• D. $\sqrt{45}M{R}^2$

Answer 1

The correct option is B $3M{R}^2$

Given,
Moment of inertia of a lamina about $x-$ axis $I_x=6M{R}^2$
Moment of inertia of a lamina about $y-$ axis $I_y=3M{R}^2$
We know that, lamina lies in $y-z$ plane.

$\therefore$ Using perpendicular axis theorem
$I_x=I_y+I_z$
We get,
$I_z=I_x-I_y=6M{R}^2-3M{R}^2$
$=3M{R}^2$