Final answer:
The acceleration of the point of contact for a ring rolling without slipping on a horizontal plane is zero because that point is instantaneously at rest with respect to the ground, even though the object itself has an overall acceleration 'a'.
Step-by-step explanation:
The question pertains to the concept of rolling motion in physics, specifically analyzing the situation of a ring rolling without slipping on a horizontal plane. When an object rolls without slipping, the point of contact with the surface has zero velocity relative to that surface, which implies that this point is instantaneously at rest. However, if the object has acceleration a, the point of contact does not remain at this rest position. Since the question mentions both velocity v and acceleration a, one might think that the point of contact is moving.
However, the key concept is that for an object rolling without slipping, the point of contact is momentarily static. Therefore, the acceleration of the point of contact with the ground is zero because it is neither moving forward nor backwards in the reference frame of the ground at that instant. Answer choices (a), (b), (c), and (d) suggest various fractions of a, but since the correct answer is that there is no acceleration at the point of contact (since it's momentarily at rest), by process of elimination none of the provided options are correct.