Final answer:
The large ball with the same velocity as the small ball has greater momentum because momentum is the product of mass and velocity, and the larger ball has more mass.
Step-by-step explanation:
Regarding the question of whether a large ball or a small ball with the same velocity has greater momentum, the answer lies in the formula for momentum: momentum (p) is equal to mass (m) multiplied by velocity (v). Given that the balls have the same velocity but different masses, the ball with the larger mass will have the greater momentum. This is because momentum is directly proportional to the mass when velocity is constant.
The larger ball has more mass, so even though the velocity is the same for both balls, the large ball carries more momentum. On the other hand, if two objects have the same momentum but different masses, the object with the smaller mass must have a greater velocity to compensate—here, the smaller mass would have the higher kinetic energy. Whereas, if two objects have the same kinetic energy, the object with the larger mass will have less velocity and thus, lesser momentum compared to the smaller mass object which would have a higher velocity.