A uniform disk is being pulled by a force F through a string attached to its center of mass. Assume
that the disk is rolling smoothly without slipping. At a certain instant of time, in which region of the
disk (if any) is there a point moving with zero total acceleration?
A Region I
B Region II
C Region III
D Region IV
E All points on the disk have a nonzero acceleration
1. To determine the region of the disk where a point has zero total acceleration, we need to consider the different components of acceleration acting on the disk. These components are:
   - Tangential acceleration vector, $\vec{a_t}$, due to the rolling motion.
   - Horizontal acceleration vector, $\vec{F}$, due to the applied force.
   - Centripetal acceleration vector, $\vec{a_r}$, due to the rotational motion.

2. We need to find a point where the vector sum of these accelerations is zero, i.e., $\vec{a_t} + \vec{F} + \vec{a_r} = \vec{0}$.

3. Let's analyze the accelerations in each quadrant of the disk:
   - **Quadrant I**: 
     - $\vec{a_t}$ is to the right and down.
     - $\vec{F}$ is strictly horizontal (to the right).
     - $\vec{a_r}$ is to the left and down.
     - The net vector has a nonzero $y$-component (downward).

   - **Quadrant II**: 
     - $\vec{a_t}$ is up and to the right.
     - $\vec{F}$ is strictly horizontal (to the right).
     - $\vec{a_r}$ is to the right and down.
     - The net vector has a nonzero $x$-component (rightward).

   - **Quadrant III**: 
     - $\vec{a_t}$ is up and to the left.
     - $\vec{F}$ is strictly horizontal (to the right).
     - $\vec{a_r}$ is up and to the right.
     - The net vector has a nonzero $y$-component (upward).

   - **Quadrant IV**: 
     - $\vec{a_t}$ is down and to the left.
     - $\vec{F}$ is strictly horizontal (to the right).
     - $\vec{a_r}$ is up and to the left.
     - The net vector can be zero if the magnitudes and directions of $\vec{a_t}$, $\vec{F}$, and $\vec{a_r}$ are such that they cancel each other out.

4. Therefore, in Quadrant IV, it is possible to find a point where the vector sum of the tangential, horizontal, and centripetal accelerations is zero.

The final answer is $\boxed{\text{(D) Region IV}}$.