Four point masses each of value m, are placed at the corners of a square ABCD of side l, The moment of inertia of the system about an axis passing throught A and parallel to BD is

Four point masses each of value m, are placed at the corners of a squa

1.	Four point masses each of value m, are placed at the corners of a square ABCD of side l, The moment of inertia of the system about an axis passing throught A and parallel to BD is
Answer» `sqrt(3) ml^(2)` `3 ml^(2)` `ml^(2)` `2 ml^(2)` SOLUTION :AS it is clear from the FIGURE, `AC=BD=sqrt(l^(2)+l^(2))=sqrt(2)l` Moment of inertia of four point masses about BD `I_(BD)=m((lsqrt(2))/(2))^(2)+mxx0+m((lsqrt(2))/(2))^(2)+mxx0` `I_(BD) = ml^(2)` Applying the theorem of parallel axis, `I_(xy)=I_(BD)+M(AO)^(2)=ml^(2)+4m((l)/(sqrt(2)))^(2)=3ml^(2)`.