if the external forces and the internal forces corresponding to an ensemble of particles are conservative. then referring to the potential that gives rise to the interaction force as Vij .. we consider that it is a function of the displacement vector |ri-rj| in order to follow the strong law of action and rtn .

how this assumption makes the interaction force a central force? ie it follows the strong law of action and rtn.

secondly.. what do you mean by grad(Vij)? and why is it equal to f*(ri-rj) where f is a scaler.. (1)

by (grad)i(Vij) we mean derivative wrt to ri.. but what exactly do we mean only by grad.. i know it will be wrt to r.. but how do we arrive at (1)