Final answer:
The solid sphere, with a smaller moment of inertia, would spin faster than the hollow sphere when the same torque is applied to each. The hollow sphere has a greater rotational kinetic energy due to its larger moment of inertia.
Step-by-step explanation:
When comparing the inertia of a solid sphere and a hollow sphere, it is important to understand the concept of moment of inertia, which is a measure of how difficult it is to change the rotational motion of an object. The hollow sphere has a larger moment of inertia than a solid sphere of the same mass and radius because more of its mass is distributed farther from its axis of rotation. If the same torque is applied to both a solid sphere and a hollow sphere, the solid sphere would spin faster because it has a smaller moment of inertia and thus requires less torque to achieve the same angular acceleration.
In rotational motion, the kinetic energy is dependent on the moment of inertia and angular velocity. Since both spheres are rotating at the same rate, the hollow sphere has a greater rotational kinetic energy due to its larger moment of inertia.