(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))`.
(b) Prove the theorem of parallel axes.
(Hint : If the centre of mass of a system of n particles is chosen to be the origin `summ_(i)r_(i)=0`).

Explanation

(a) 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)`
If the centre of mass of a system of n particles is chosen to be the origin `Sigmam_(i)r_(i)=0`.