A thin uniform rectangular plate of mass 2 ~kg is placed in x y -plane as shown in figure. The moment of inertial about x -axis is I_ x =0.2 kgm ² and the moment of inertia about Y -axis is I_ y =0.3 kgm ² . The radius of gyration of the plate about the axis passing through O and perpendicular to the plane of the plate is

Step-by-step solution

Given, mass, M=2 ~kg aligned &I_ x =0.2 ~kg - m ² &I_ y =0.3 ~kg - m ² aligned and I_ y =0.3 ~kg - m ² According to the perpendicular axis theorem, the moment of inertia of the rectangular plate about an axis passing through O and perpendicular to the plane of plate is I=I_ x +I_ y =0.2+0.3=0.5 ~kg ~m ² Also, I=M k² where, k= radius of gyration. k= I M = 0.5 2 = 0.25 =0.5 ~m or 50 ~cm