An isosceles triangular piece is cut a square plate of side `l`. The piece is one-fourth of the square and mass of the remaining plate is `M`. The moment of inertia of the plate about an axis passing through `O` and perpendicular to its plane is

Options

A. `(Ml^(2))/6`
B. `(Ml^(2))/12`
C. `(Ml^(2))/24`
D. `(Ml^(2))/3`

Answer

A

Explanation

Mass of each of the four parts `=M/3`
Mass of the plane including the cut piece `=(4M)/3`
Moment of inertia of the whole plate (including the cut piece ) about the said axis `=((4M)/3)(l^(2))/6`
Now moment of inertia of the remaining portioin should be `3/4` of the above `=Ml^(2)//6`