[UPSC CSE 1996] Central Force Motion and Gravitation (Q116, 20M)

A Particle of mass m, moving with an initial velocity v_0 is acted on by a central repulsive inverse-square force, F = \frac{k}{r^2}. Show that the scattering angle \phi depends on the impact parameter b as \cot \left(\frac{\phi}{2}\right) = \frac{m v_0^2}{k} b.