Final answer:
Comparing the magnitudes of the momentum p₁ and p'₂ after the collision of two balls, we concur that typically p₁ would be greater than p'₂, based on the principle of conservation of momentum.
Step-by-step explanation:
When considering the collision between a moving ball (with momentum p₁) and a stationary ball, the principle of conservation of momentum applies, assuming no external forces are acting on the system (such as friction, air resistance, etc.). In an isolated system, the total momentum before the collision is equal to the total momentum after the collision. This is a fundamental concept in physics known as the conservation of linear momentum.
In the given scenario, the first ball has an initial momentum of p₁, and the second ball is stationary, meaning its initial momentum is zero. After the collision, the first ball's momentum changes to p'₁, and the second ball's momentum becomes p'₂. Since the directions of p₁, p'₁, and p'₂ are the same, we can directly compare their magnitudes. To maintain conservation of momentum, the sum of p'₁ and p'₂ must be equal to the initial momentum p₁ (assuming no external forces).
Therefore, the magnitude of momentum p'₂ imparted to the second ball must be less than or equal to the initial momentum p₁. If the first ball continues to move after the collision, which means p'₁ is not zero, then p'₂ must be smaller than p₁ because p₁ = p'₁ + p'₂. The answer cannot be determined with the information given if we do not know the masses of the balls or the specifics of the collision. However, typically in such collisions, some momentum is retained by the first ball, making option (c) p₁ is greater than p'₂ the likely scenario.