Final answer:
In an object rolling without slipping, the linear velocity of the top point is twice that of the object's center, and the bottom point has a velocity of zero relative to the ground.
Step-by-step explanation:
When an object is rolling without slipping, we can analyze the relationship between the linear speeds at different points on the object. The linear velocity of the top point of the object, v_top, is twice the linear velocity of the center, v_center, because the top point is moving in the same direction as the object's translation and has additional velocity due to rotation. On the other hand, the point of contact at the bottom, v_bottom, is momentarily at rest relative to the ground as it's the pivot point for the rotation. Therefore, the correct relationship is a) v_top = 2v_center, v_bottom = 0.
This comes from the logic that at any given instant, the point where the rolling object contacts the ground is not moving relative to the surface it is on, so v_bottom = 0. Simultaneously, the center of the object moves with linear speed v_center = Rw, where R is the radius of the object and w is the angular velocity around its axis. Accordingly, the top point of the object, which is a distance 2R away from the bottom point, moves with v_top = 2v_center due to both the object's translation and rotation.