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

The moment of inertia is a physical quantity that describes how easily a body can be rotated about a given axis. It is a rotational equivalent of mass, which describes an object's resistance to translational motion. Inertia is the property of matter which resists change in its state of motion.

Complete step by step solution:
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 to increase speed.

Both the spheres are of the same size and weight. However, the hollow sphere's weight is 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 its mass spread evenly throughout, so much of the weight is close to the center, and only some part of it is near the surface. That means that the solid sphere has a lower moment of inertia.

Since the mass of both is the same, the force of gravity on both is also 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.

Note: 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, some of that energy is rotational kinetic energy. Not all of the energy is rotational kinetic energy. Not all of the energy is converted to velocity.