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

Options

A. `(4)/(3)Ml^(2)`
B. `(Ml^(2))/(3)`
C. `(Ml^(2))/(6)`
D. `(2)/(3)Ml^(2)`

Answer

A

Explanation

Moment of inertioa of one rod
`I.=I_(cm)+M((1)/(2))^(2)=(Ml^(2))/(12)+(Ml^(2))/(4)=(4Ml^(2))/(12)=(Ml^(2))/(3)`
Moment of inertia of system
`I=4I.=(4Ml^(2))/(3)`