A uniform disc has a radius of gyration equal to its radius r about a line perpendicular to the disc. Determine the distance of this line from the centre.

Step-by-step solution

Let the mass of the uniform disc be M and its radius be r . The moment of inertia of the disc about an axis passing through its centre and perpendicular to its plane is I_ cm = 1 2 M r^2 . Let the required axis be at a distance d from the centre. By the theorem of parallel axes, the moment of inertia about this axis is: I = I_ cm + M d^2 = 1 2 M r^2 + M d^2 The radius of gyration k about this axis is given as r . Therefore, the moment of inertia can also be written as: I = M k^2 = M r^2 Equating the two expressions