A boy swings a ball attached to a string in a horizontal circle above his head. If the string suddenly snaps, what path will the ball follow immediately after the break?

Introduction / Context:
Circular motion is a classic topic in physics that illustrates how forces affect the direction of motion. When an object moves in a circle, its direction is constantly changing, even if its speed is constant. This question uses the simple example of a ball on a string being swung in a horizontal circle to test your understanding of what happens when the centripetal force is suddenly removed by snapping the string.

Given Data / Assumptions:

• A ball is attached to a string and is moving in a horizontal circular path.
• The string provides the centripetal force needed to keep the ball moving in the circle.
• At a particular instant, the string snaps (breaks).
• Air resistance is neglected for simplicity, and gravity acts downward.

Concept / Approach:
In uniform circular motion, the velocity of the ball at any instant is tangential to the circle. The string pulls the ball toward the centre, providing centripetal force and constantly changing the direction of the velocity. If the string breaks, this inward force immediately disappears. According to Newton's first law, the ball will then continue in a straight line along the direction of its velocity at the instant of the break, which is along the tangent to the circle. Gravity will then make it follow a curved path downward, but the initial direction is tangential.

Step-by-Step Solution:
Step 1: Before the string snaps, the ball is in circular motion, so its instantaneous velocity at any point is tangential to the circle. Step 2: The string provides centripetal force, pulling the ball toward the centre and changing the direction of motion but not necessarily the speed. Step 3: At the moment the string snaps, the centripetal force vanishes abruptly. Step 4: In the absence of this inward force, the ball must obey Newton's first law and move in a straight line in the direction of its velocity at that instant. Step 5: Therefore, immediately after the break, the ball moves along the tangent to the circle at the point of snapping, and then gravity causes it to curve downward and eventually fall to the ground.

Verification / Alternative check:
This behaviour is similar to what you observe in many real situations, for example when a stone is whirled on a string and then released. It does not fly toward the centre of the circle or continue around the same circular path; it flies off tangentially. Diagrams in physics textbooks depicting circular motion always show the velocity vector as tangent to the circle. Removing the inward pull means the object can no longer bend its path toward the centre and must instead follow the straight-line path of the velocity vector at that instant.

Why Other Options Are Wrong:
It will move straight toward the centre of the circle and then fall down: This would require a force directed toward the centre, but once the string snaps, that force no longer exists.

It will fall straight down at the same place where the string breaks: Gravity acts downward, but the ball already has horizontal velocity, so it cannot simply drop vertically without horizontal motion.
It will spiral inward toward the centre before falling down: A spiral motion toward the centre would require a changing inward force, which is absent once the string has broken.

Common Pitfalls:
A common mistake is to think that because the ball was "pulled" toward the centre before the break, it will continue to move inward after the string snaps. Another misunderstanding is to ignore the ball's existing horizontal velocity and imagine that gravity makes it fall straight down. Remember that motion in one direction does not cancel just because a force stops; the ball keeps the velocity it already has at the instant the force is removed.

Final Answer:
When the string snaps, the ball will move along the tangent to the circle at the breaking point and then fall down.