What is the maximum amount of rope wound on the axle when the golf ball drops?

The correct answer is that the maximum amount of rope wound on the axle is determined by the radius of the axle and the distance the golf ball drops. This relationship can be understood through the principles of rotational motion and linear displacement.

When the golf ball drops, gravity pulls it downward, and as it does so, the rope unwinds from the axle. The key factors at play here are the distance that the golf ball drops and the radius of the axle around which the rope is wound. The distance the ball falls directly translates into the length of rope that will be wound onto the axle given the axle's radius.

As the golf ball descends, it creates a linear distance equal to the length of rope wound on the axle, which can be calculated by the formula that relates linear distance to angular distance: ( \text{Length of rope} = \text{Radius} \times \text{Angle of rotation} ). The more the ball drops, the greater the angle of rotation of the axle. Therefore, regardless of the mass of the golf ball, the total length of rope wound on the axle is fundamentally a function of both how far the ball drops and how large the axle is.

This makes options that suggest the length is constant,