Final answer:
For objects with the same momentum, the object with the small mass will have a larger kinetic energy as it has a higher velocity to compensate for its smaller mass. Conversely, if the objects have the same kinetic energy, the object with a small mass will have a larger momentum due to its higher velocity.
Step-by-step explanation:
An Object with Small Mass and Large Mass Have the Same Momentum
When an object that has a small mass and an object that has a large mass have the same momentum, it means their mass and velocity are inversely proportional. Since momentum (p) is the product of mass (m) and velocity (v), given by the equation p = m \times v, and kinetic energy (KE) is given by the equation KE = \frac{1}{2}m \times v^2, for the same momentum, an object with smaller mass must have a higher velocity to compensate.
Therefore, since the velocity is squared in the kinetic energy formula, the object with the smaller mass will have a larger kinetic energy because it will have a disproportionately higher velocity to maintain the same momentum as the object with larger mass. The answer to the question is (a) object with small mass.
Same Kinetic Energy and Different Masses
If an object that has a small mass and an object that has a large mass have the same kinetic energy, the object with the small mass must have a higher velocity since kinetic energy depends on the square of the velocity. In this case, the object with the small mass would have a larger momentum because its high velocity would contribute more to the momentum than the large mass of the other object at a lower velocity.