When two spheres of different masses are pushed, the outcome depends on the nature of the impact, whether elastic or inelastic. In a purely elastic collision, the left sphere (mass m) will transfer some of its momentum to the right sphere (mass 2m) upon impact. The left sphere will move to the right, while the right sphere will begin to move as well, but at a slower speed due to its greater mass. The final velocities of both spheres can be calculated using conservation of momentum and kinetic energy principles. The interaction illustrates fundamental concepts in physics regarding motion and collisions.