A square plate of mass `M` and edge `L` is shown in the figure. The moment of inertia of the plate about the axis in the plane of plate and passing through one of its vertex making an angle `15^@` horizontal is `

Options

A. `(ML^(2))/12`
B. `(11 ML^(2))/24`
C. `(7ML^(2))/12`
D. `(10 ML^(2))/24`

Answer

B

Explanation

From diagram, we get `x=AO sin 60^(@)`
`=L/(sqrt(2))xx(sqrt(3))/2, I_(z)=(ML^(2))/6, I_(x)=I_(y)=(ML^(2))/12`
`I_(AB)=(ML^(2))/12+Mx^(2)`