Central-force motion — UPSC Physics Optional CSE 2012 Paper I

A particle is moving in a central force field on an orbit given by r = ke^{\alpha\theta}, where k and \alpha are positive constants, r is the radial distance and \theta is the polar angle.

(i) Find the force law for the central force field.

(ii) Find \theta(t).

(iii) Find the total energy.