Four identical thin rods each of mass `M` and length `l`, from a square frame. Moment of inertia of this frame about an axis through the centre of the square and perpendicular to its plane is

Options

A. `(4)/(3) Ml^2`
B. `(2)/(3) Ml^2`
C. `(13)/(3) Ml^2`
D. `(1)/(3) Ml^2`

Answer

A

Explanation

(a) The moment of inertia of rod about an axis through its centre of mass and perpendicular to rod + (mass of rod) xx (perpendicular distance between two axes)
=`(Ml^2)/(12) + M((l)/(2))^2 = (Ml^2)/(3)`
Moment of inertia of the system `= (Ml^2)/(3) xx 4`
=`(4)/(3) Ml^2`.