Final answer:
When two objects have the same kinetic energy, one with a smaller mass must have a higher velocity to compensate. For momentum, which is mass times velocity, both objects could have the same momentum despite their difference in mass. Without additional information about their velocities, we cannot determine which has the larger momentum.
Step-by-step explanation:
An object that has a small mass and an object that has a large mass have the same kinetic energy. To determine which mass has the largest momentum, we need to recall that kinetic energy (KE) and momentum (p) are related differently to mass (m) and velocity (v). While KE = 1/2 mv2, momentum is given by the equation p = mv. Given that the kinetic energy is the same, and kinetic energy depends on the square of the velocity, the object with a smaller mass must have a higher velocity (since KE = 1/2 msmallvsmall2 = 1/2 mlargevlarge2).
If we compare the momentum of the two objects, the small mass object's higher velocity compensates for its smaller mass, and similarly, the large mass object's larger mass compensates for its lower velocity. Thus, when kinetic energy is the same, their momenta can also be the same. This means that both objects can have the same momentum, depending on their velocities. To clearly answer the question, because the kinetic energy is the same for both, we cannot determine which has the larger momentum without additional information regarding their velocities. Therefore, the answer is (d) Cannot be determined.