If $${v_e}$$ is escape velocity and $${v_o}$$ is orbital velocity of a satellite for orbit close to the earth's surface, then these are related by

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

Three masses are placed on the x-axis : 300 g at origin, 500 g at x = 40 cm and 400 g at x = 70cm. The distance of the centre of mass from the orgin is :

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