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 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

A particle of mass m is released from rest and follows a parabolic path as shown. Assuming that the displacement of the mass from the origin is small, which graph correctly depicts the position of the particle as a function of time ?