The figure shows a top view of a ball on the end of a string traveling counterclockwise in a circular path. The speed of the ball is constant. If the string should break at the instant shown, the path that the ball would follow is
A) 1
B) 2
C) 3
D) 4
E) impossible to tell from the given information.

Question

The figure shows a top view of a ball on the end of a string traveling counterclockwise in a circular path. The speed of the ball is constant. If the string should break at the instant shown, the path that the ball would follow is 
A) 1 
B) 2 
C) 3 
D) 4 
E) impossible to tell from the given information.

Quizplus · Accepted Answer

Since there is a constant forward speed, the ball will continue to move in the direction tangent to the circle at the point just before the string breaks. This means that the ball will move in a straight line, perpendicular to the radius of the circle at that point. Looking at the figure, it can be seen that the radius at the point just before the string breaks is perpendicular to the segment connecting the center of the circle to the point where the string is attached. Following this segment backwards, it can be seen that it intersects the circle in two places. These two points are the possible locations where the ball would end up if the string were to break at the instant shown. Therefore, there are two possible paths for the ball, which corresponds to choice B.

The Figure Shows a Top View of a Ball on the End