Final answer:
The sand forms a conical pile, and for the motion on an inclined plane, a solid sphere would roll down faster than a hollow cylinder. A hollow cylinder reaches a greater height than a hollow sphere when both roll up an incline with the same initial velocity.
Step-by-step explanation:
The sand falling from a chute and forming a pile where the height is 4/3 of its base diameter indicates that the shape is conical. This is because only a cone has a height proportional to its base diameter in real-world scenarios where materials like sand form piles. The answer to the question is: c) Cone.
When examining the dynamics on an inclined plane, a hollow cylinder, because of its mass distribution further from the axis, would roll down slower compared to a solid sphere that has a more evenly distributed mass. For the case of the hollow sphere and the hollow cylinder of the same radius and mass rolling up an incline, the hollow cylinder would reach a greater height before stopping because it has a larger moment of inertia, which means it can store more rotational energy at the same center of mass velocity compared to the hollow sphere.