If the potential energy between two molecules is given by
U = $$ - {A \over {{r^6}}} + {B \over {{r^{12}}}}$$,
then at equilibrium, separation between molecules, and the potential energy are :

A person pushes a box on a rough horizontal plateform surface. He applies a force of 200 N over a distance of 15 m. Thereafter, he gets progressively tired and his applied force reduces linearly with distance to 100 N. The total distance through which the box has been moved is 30 m. What is the work done by the person during the total movement of the box?

A particle is moving unidirectionally on a horizontal plane under the action of a constant power supplying energy source. The displacement (s) - time (t) graph that describes the motion of the particle is (graphs are drawn schematically and are not to scale) :

Consider a force $$\overrightarrow F = - x\widehat i + y\widehat j$$ . The work done by this force in moving a particle from point A(1, 0) to B(0, 1) along the line segment is : (all quantities are in SI units)