Energy changes in a head-on collision between two unequal Plummer model stellar systems (galaxies) are studied analytically under the impulsive approximation. The variation of the disruptive effects within and the mass escape from systems widely differing in mass and scalelength ratios are determined and some physical implications regarding the dynamical stability of the systems undergoing head-on collisions are indicated. It is found that if two systems differ considerably in size, both systems generally survive the collision if (i) the mass of the bigger is greater than about six times the mass of the smaller and (ii) the density of the smaller is more than about twenty-five times the entity of the bigger system, when the velocity at minimum separation is equal to the parabolic velocity of escape.