A particle of mass m approaches a region of force starting from `r=+infty` The potential energy function in terms of distance r from the origin is given by,
`U(r) = K/(2a^(3))(3a^(2)-r^(2)) for 0 lt r lt a`
`=K//r for r gt a`
(a) Derive the force F(r) and determine whether it is repulsive or attractive.
(b) With what velocity should the particle start at `r=infty` to cross over to other side of the origin.
(c) If the velocity of the particle at `r= infty` is `sqrt((2K)/(am))` towards the origin describe the motion.

Answer

`[(a) repulsive (b) `sqrt((3K)/(am))]`