The moment of inertia of a system of four rods, each of length l and mass m, about the axis shown is:

Options

A. `sqrt(3) ml^(2)`
B. `3 ml^(2)`
C. `ml^(2)`
D. `2 ml^(2)`

Answer

B

Explanation

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)`.