A particle of mass m approaches a region of force starting from `r=+infty` The potential energy
Channel: Doubtnut
Date: 2021-11-02

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.