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

Answer

D

Explanation

`I_(z)=4[(Ml^(2))/(12)+M((l)/(2))^(2)]`
`=4[(Ml^(2))/(12)+(Ml^(2))/(4)]`
`=4Ml^(2)((1+3)/(12))`
`=4Ml^(2)((1+3)/(12))`