The potential energy of a particle in a force field is $$U = {A \over {{r^2}}} - {B \over r}$$ where A and B are positive constants and r is the distance of particle from the centre of the field. For stable equilibrium, the distance of the particle is

A solid cylinder of mass 3 kg is rolling on a horizontal surface with velocity 4 m s^$$-$$1. It collides with a horizontal spring of force constant 200 N m^$$-$$1. The maximum compression produced in the spring will be

A mass m moving horizontally (along the x-axis) with velocity $$v$$ collides and sticks to a mass of 3m moving vertically upwards (along the y-axis) with velocity 2$$v$$. The final velocity of the combination is

A body projected vertically from the earth reaches a height equal to earth's radius before returning to the earth. The power exerted by the gravitational force is greatest