Circular Disc and Concentric circles

On a disc of radius R a concentric circle of radius R//2 is drawn. The disc is free to rotate about a frictionless fixed axis through its center and perpendicular to plane of the disc. All three forces ( in plane of the disc ) shown in figure are exerted tangent to their respective circular periphery. The magnitude of the net torque ( about centre of disc ) acting on the disc is :

On a disc of radius R a concentric circle of radius R//2 is drawn. The disc is free to rotate about a frictionless fixed axis through its center and perpendicular to plane of the disc. All three forces ( in plane of the disc ) shown in figure are exerted tangent to their respective circular periphery. The magnitude of the net torque ( about centre of disc ) acting on the disc is :

On a disc of radius R a concentric circle of radius R//2 is drawn. The disc is free to rotate about a frictionless fixed axis through its center and perpendicular to plane of the disc. All three forces ( in plane of the disc ) shown in figure are exerted tangent to their respective circular periphery. The magnitude of the net torque ( about centre of disc ) acting on the disc is :

If a circular concentric hole is made on a disc then about an axis passing through the centre of the disc and perpendicular to its plane

If a circular concentric hole is made on a disc then about an axis passing through the centre of the disc and perpendicular to its plane

The ratio of the radii of gyration of a circular disc and a circular ring of the same radii about a tangential axis perpendicular to plane of disc or ring is

The ratio of the radii of gyration of a circular disc and a circular ring of the same radii about a tangential axis perpendicular to plane of disc or ring is

From a uniform circular disc of diameter d,a circular disc of diameter d//6 and having centre at a distance d//4 from the centre of the disc is scooped out. Determine the centre of mass of remaining portion.