Final answer:
The hollow sphere reaches a greater height before stopping because it has a smaller moment of inertia than the hollow cylinder, making it more efficient at conserving its kinetic energy during the climb.
Step-by-step explanation:
When a hollow sphere and a hollow cylinder of the same radius and mass roll up an incline without slipping, the object that reaches a greater height before stopping is determined by their moments of inertia. The moment of inertia is a measure of how mass is distributed relative to the axis of rotation, affecting how the object rolls. A hollow sphere has a smaller moment of inertia compared to a hollow cylinder due to the way the mass is distributed.
Since both objects have the same mass, radius, and initial center of mass velocity, the one with the smaller moment of inertia (hollow sphere) will convert more of its kinetic energy into rotational energy, thus retaining more translational kinetic energy. Consequently, the hollow sphere will reach a greater height before coming to a stop, as it is more efficient in conserving its initial kinetic energy. This conclusion is independent of the incline angle, as long as no other forces such as friction or air resistance are considered.