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

Four identical thin rods each of mass M and length l from a square fra

1.	Four identical thin rods each of mass M and length l from a square frame. Moment of inerita of this frame about an axis through the centre of the square and perpendicular to its plane is ……………
Answer» `(2)/(3)ML^(2)` `(13)/(3)Ml^(2)` `(1)/(3)Ml^(2)` `(4)/(3)Ml^(2)` SOLUTION : Moment of inertia of a rod of mass M and length l about an axis passing through the midpoint of rod and perpendicular the length of rod is `I=(1)/(12)Ml^(2)` Now any rod of frame away from O to `(l)/(2)` then according to parallel axis theorem. Its moment of inertia `I_(1)=I+Md^(2)` `=(1)/(12)Ml^(2)+(Ml^(2))/(4)` `=(4ml^(2))/(12)=(1)/(3)ml^(2)` TOTAL moment of inertia of frame = sum of moment of inertia of all four rods `=4xx(1)/(3)Ml^(2)` `=(4)/(3)Ml^(2)`