Answer: b. The tension force of the string will be equal to the weight of the ball
Despite the fact that the ball is not moving, that doesn't mean there aren't any forces being applied. Instead, we have the force of gravity pulling down which causes the object to have apparent weight. In the opposite direction, the tension in the string pulls up to counterbalance the force of gravity.
If the force of gravity is stronger than the tension in the string, then the ball would accelerate downward and move downward. On the flip side, if the tension force in the string was stronger than the force of gravity, then the ball would move upward. However, the ball is stationary so the two forces are equally at a stalemate. You can think of it like a vertical tug of war where both sides are tied.