Question

A square plate lies in the xy plane with its centre at the origin and its edges parallel to the x and y axes. Its moments of inertia about the x, y and z axes are $I_x,I_y,and{I}_z$ respectively, and about a diagonal it is $I_D$.

• A. $I_x=I_y=\frac{1}{2}{I}_z$
• B. $I_x=I_y=2I_z$
• C. $I_D=I_x$
• D. $I_D=I_z$

Answer 1

The correct option is A $I_x=I_y=\frac{1}{2}{I}_z$

We have $I_x$ and $I_y$ equal as it is a square plate. Now using perpendicular axis theorem we have $I_x+I_y=I_z$. Thus we get $I_x=I_y=\frac{1}{2}{I}_z$