The moment of inertia of uniform circular disc is maximum about an axis perpendicular to the disc and passing through point

A ring and a disc roll on horizontal surface without slipping with same linear velocity. If both have same mass and total kinetic energy of the ring is 6 J then total kinetic energy of the disc is

A solid metallic sphere of radius ' $R$ ' having moment of inertia '$I$' about diameter is melted and recast into a solid disc of radius ' $r$ ' of a uniform thickness. The moment of inertia of a disc about an axis passing through its edge and perpendicular to its plane is also equal to '$I$'. The ratio $\frac{r}{R}$ is

A particle of mass ' m ' is rotating in a circular path of radius ' $r$ '. Its angular momentum is ' $L$ ' The centripetal force acting on it is ' $F$ '. The relation between ' $F$ ', ' $L$ ', ' $r$ ' and ' $m$ ' is