A 0.21 kg ball on a string is whirled on a vertical circle at a constant speed. When the ball is at the three o'clock position, the tension is 18 N.

(c) Is the tension in the string greater when the ball is at the twelve o'clock position or when it is at the six o'clock position, or is the tension the same at both positions?

The tension is the same at both positions.

The tension is greater at the six o'clock position.

The tension is greater at the twelve o'clock position.

and your thinking is...?

To determine whether the tension in the string is greater at the twelve o'clock position, the six o'clock position, or the tension is the same at both positions, we need to consider the forces acting on the ball at each position.

At the twelve o'clock position, the tension in the string is directed towards the center of the circle, acting as the centripetal force to keep the ball in circular motion. This tension force can be calculated using the equation:

Tension = (mass * velocity^2) / radius

At the six o'clock position, the tension in the string will be directed away from the center of the circle. This tension force is also acting as the centripetal force. To calculate this tension force, we need to take the net force acting on the ball into account. The net force is given by the equation:

Net force = tension force - weight

Weight = mass * gravitational acceleration

If the net force is positive, it means the tension force is greater than the weight and the ball will continue moving in a circular path. If the net force is negative, the tension force is smaller than the weight, and the ball will lose contact with the string and fall down.

By comparing the equations for the tension force at the twelve o'clock and six o'clock positions, we can see that the tension force at the twelve o'clock position is greater. This is because the mass, velocity, and radius are the same at both positions, but the weight is always acting downwards regardless of the position.

Therefore, the correct answer is:

The tension is greater at the twelve o'clock position.