A square is made by joining four rods each of mass `M` and length `L`. Its moment of inertia about an axis PQ, in its plane and passing through one one of its corner is

Options

A. `2/3ml^(2)`
B. `2ml^(2)`
C. `3ml^(2)`
D. `8/3ml^(2)`

Answer

D

Explanation

Moment of inertia about `2`

` I_(2)=4((ml^(2))/3sin^(2)45^@)=(2ml^(2))/3`
Apply perpendicular axis theorem
`I_(1)=I_(2)+mh^(2)`
`=(2ml^(2))/3+4m(1/sqrt(2))^(2)=8/3ml^(2)`