Four thin rods of same mass 'M' and same length 'l', form a square as shown in t

Question

Four thin rods of same mass 'M' and same length 'l', form a square as shown in the figure. Moment of inertia of this system about an axis through centre O and perpendicular to its plane is

Options:

A . 43Ml2.

B . Ml23

C . Ml26

D . 23Ml2.

Answer: Option A
:
A
Moment of inertia of rod AB about point

P = \frac{1}{12} M l^{2}

M.I. of rod AB about point

O = \frac{M l^{2}}{12} + M {(\frac{1}{2})}^{2} = \frac{1}{3} M l^{2}

[by the theorem of parallel axis]
and the system consists of 4 rods of similar type so by the symmetry

I_{S y s t e m} = \frac{4}{3} M l^{2} .

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