Four indentical thin rods each of mass M and length l, form a square frame. Momentum of inertia of this frame about an axis through the centre of the square and perpendicular to its plane is:

Options

(a) 2/3 MI²
(b) 13/3 MI²
(c) 1/3 MI²
(d) 4/3 MI²

Correct Answer:

4/3 MI²

Explanation:

Moment of inertia of oa thin rod of length l about an axis passing through centre and perpendicular to the rod = 1/12 MI².
Thus, moment of inertia of the frame.
MI² / 12 + MI² / 4 = 4 MI² / 12 = MI² / 3
Total M.I. = 4/3 MI²