The ratio of radii of gyration of a circular ring and a circular disc, of the same mass and radius, about an axis passing through their centres and perpendicular to their planes are

A rod PQ of mass M and length L is hinged at end P. The rod is kept horizontal by a massless string tied to point Q as shown in figure. When string is cut, the initial angular acceleration of the rod is

A small object of uniform density rolls up a curved surface with an initial velocity 'v'. It reaches upto a maximum height of $${{3{v^2}} \over {4g}}$$ with respect to the initial position. The object is

A circular platform is mounted on a frictionless vertical axle. Its radius R = 2 m and its moment of inertia about the axle is 200 kg m². It is initially at rest. A 50 kg man stands on the edge of the platform and begins to walk along the edge at the speed of 1 ms^$$-$$1 relative to the ground. Time taken by the man to complete one revolution is