Question

If a solid sphere and a hollow sphere are released from the top of a rough inclined plane, which sphere will reach the bottom first.

Answer 1

I assume this question comes from a physics course study of rotating objects, so you have probably heard the term "moment of inertia" before. In layman's terms, moment of inertia is a measurement of how much a spinning object weighs multiplied by how far away the parts of the object are from the center of rotation. The larger the moment of inertia, the harder it is to get something spinning. This is why a figure skater can spin faster when she pulls her arms and legs inward; she is reducing her moment of inertia.
Getting back to the question of the rolling spheres. Both are the same size and weight. However, the hollow sphere's weight is all packed tightly near the surface of the sphere, away from the center. More of the sphere's mass is far away from the center of rotation, so the hollow one has a big moment of inertia. On the other hand, the solid sphere has it's mass spread evenly throughout, so much of the weight is close to the center, and only part of it is near the surface. That means that the solid sphere has a lower moment of inertia.
Since the mass of both are the same, the force of gravity on both is exactly the same. Since the hollow sphere has a greater moment of inertia, this force will cause it to accelerate more slowly than the solid one. Therefore, the solid ball will reach the bottom first.
A few final thoughts: Since the mass and outside shape of both are the same, air resistance is the same. Also, both will have the same energy when they reach the bottom, but remember, some of that energy is rotational kenetic energy. Not all of the energy is converted to velocity.