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

Two discs are rotating about their axes, normal to the discs and passing through the centres of the discs. Disc D₁ has 2 kg mass and 0.2 m radius and initial angular velocity of 50 rad s^$$-$$1. Disc D₂ has 4 kg mass, 0.1 m radius and initial angular velocity of 200 rad s^$$-$$1. The two discs are brought in contact face to face, with their axes of rotation coincident. The final angular velocity (in rad s^$$-$$1) of the system 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 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