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 of its corner is

Options

A. `6ML^(2)`
B. `(4)/(3)ML^(2)`
C. `(8)/(3)ML^(2)`
D. `(10)/(3)ML^(2)`

Answer

C

Explanation

`r=(l)/(sqrt(2))+(l)/(2sqrt(2))=(2l)/(2sqrt(2))`
`I=2I_(1)+2I_(2)`
`=2(I_(1)+I_(2))`
`=2[(ML^(2))/(3)sin^(2)45^(@)+(ML^(2))/(12)sin^(2)45^(@)+Mr^(2)]`
`=(8)/(3)ML^(2)`