Which object goes farthest up the incline?

When a solid ball, solid disk, and a hoop with the same mass and radius are set to roll without slipping up an incline with the same initial speed, the hoop goes farthest up the incline. This is because the hoop has a smaller calculated inertia of 2/3mr² compared to the solid disk, allowing it to reach a higher point on the incline.

The inertia of an object is a measure of its resistance to changes in its rotational motion. In this case, the hoop's smaller calculated inertia enables it to overcome the incline's resistance and travel further up compared to the solid ball and the solid disk.

Therefore, when considering objects with the same mass and radius rolling without slipping up an incline with the same initial speed, the one with the smaller calculated inertia, such as the hoop in this scenario, will go farthest up the incline.