# Q7.26 (a)     Prove the theorem of perpendicular axes. (Hint: Square of the distance of a point $(x,y)$  in the $x-y$     plane from an axis through the origin and perpendicular to  the plane is $x^{2}+y^{2}$).

Consider the figure given below:

The moment of inertia about the x-axis is given by :

$I_x\ =\ mx^2$

And the moment of inertia about the y-axis is :

$I_y\ =\ my^2$

$I_z\ =\ m\left ( \sqrt{\left ( x^2\ +\ y^2 \right )} \right )^2$
or                                    $I_z\ =\ I_x\ +\ I_y$