A boy is swinging a ball attached to a string in a horizontal circle. If the string suddenly snaps at some instant, how will the ball move just after the string breaks?

Introduction / Context:
This mechanics question tests your understanding of circular motion and the concept of inertia. When an object moves in a circle, a centripetal force is needed to constantly change its direction. If this centripetal force is removed suddenly, the object does not continue in a circle but follows a new path determined by its velocity at that instant. Recognising that this path is tangential to the circle is key to answering the question correctly.

Given Data / Assumptions:

• A ball is attached to a string and is being rotated in a horizontal circle.
• The motion is uniform circular motion just before the string breaks.
• The string suddenly snaps at some point in the motion.
• Air resistance and other forces besides gravity are neglected immediately after the break.

Concept / Approach:
In uniform circular motion, the velocity of the ball is always tangential to the circle, while the centripetal force provided by the string acts towards the center. This inward force keeps changing the direction of the velocity vector. If the string breaks, the centripetal force instantly becomes zero. According to Newton first law of motion (the law of inertia), the ball will continue to move in a straight line in the direction of its velocity at that instant. That straight line is the tangent to the circle at the point where the string snapped. Gravity then acts downward, so the ball follows a projectile like path starting along that tangent.

Step-by-Step Solution:
Step 1: Identify the forces acting during circular motion: tension in the string provides centripetal force towards the center, and gravity acts vertically. Step 2: The instantaneous velocity of the ball is always along a tangent to the circular path at every point. Step 3: When the string snaps, the tension force disappears suddenly, removing the centripetal force. Step 4: By inertia, the ball will continue to move in the direction of its instantaneous velocity, which is along the tangent at the breaking point. Step 5: After that, gravity starts to pull the ball downward, causing it eventually to fall to the ground along a curved trajectory starting from the tangential direction. Step 6: Therefore, the correct description is that the ball continues along the tangent to the circle and then falls down.

Verification / Alternative check:
You can visualise a similar situation by swinging a stone tied to a string and then releasing it at some point. The stone does not fly toward the center or continue in a circle; it shoots off along a straight line path that is tangential to the circle at the release point. This behaviour is often demonstrated in physics classes and matches the prediction of Newton laws. The same principle is used in sports such as hammer throw, where the athlete swings the hammer in a circle and releases it to send it off tangentially.

Why Other Options Are Wrong:
The ball will travel towards the center is incorrect because once the string breaks, there is no inward force to pull the ball toward the center. It will fall down at the same place where the string breaks is wrong because the ball has non zero tangential velocity, so it will move horizontally before falling. None of these is incorrect because option describing tangential motion is a correct and precise statement of what happens.

Common Pitfalls:
Students sometimes think that because centripetal force was pointing towards the center just before the break, the ball will move inward when the string snaps. This ignores the difference between force and velocity direction. The velocity is tangential, not radial, in circular motion. Once the centripetal force vanishes, there is no reason for the ball to move towards the center. Remembering that velocity is always tangent to the circle and that objects move in straight lines when unforced helps avoid this error.

Final Answer:
When the string snaps, the ball will continue to travel along a tangent to the circle at the point of snapping and then fall down under gravity.