Question

the moment of inertia of a door of mass m and length 2l and width l about the axis CD in the plane of door and at an angle of 45° with x axis is?
Figure given below

Answer 1

Hey,

Moment of Inertia of a rectangular plate is M{a^2+b^2}/12  on an axis perpendicular to the plate

Here  the question meant a  rectangular plate with length a=2l and breadth=l

I=M{4l^2+l^2}/12=5/12ML^2

So I=5/12Ml^2

By using perpendicular axis theorem Moment of inertia on axis AB=1/2I=5/24Ml^2

Iab=5/24Ml^2

On the axis CD Icd=Iab Sin^2 {∅} 

Icd=5/24Ml^2Sin^2{∅}