What happens when two spheres of different masses are given a slight push?

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When a slight force F is applied to the left sphere (mass m) in contact with a right sphere (mass 2m), the outcome is determined by the nature of the impact. If the impact is purely elastic, both spheres will move after the push, with the left sphere transferring some of its momentum to the right sphere. The right sphere will move with a velocity that is dependent on the mass ratio and the initial velocity imparted by the left sphere.

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There are two spheres in contact in a row. The mass of the left one is m and the right is 2m. If there's a slight push of F to the right on the left ball. What would happen to the two balls?

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What would happen depends on the spheres, or whether it is a hard or soft impact
 
It's purely elastic.
 

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