If a string with a ball attached to it is in circular motion and the string is cut, the ball will continue to move tangentially to its previous circular path according to Newton's first law of motion, which states that an object in motion will continue moving with the same velocity unless acted upon by an external force. This phenomenon is known as the law of inertia.
When the string is cut, the centripetal force provided by the tension in the string is removed. Without this force, the ball will no longer experience the inward force necessary to maintain circular motion. As a result, the ball will move in a straight line tangent to its circular path at the moment the string was cut.
The ball will continue moving in this straight line until it is acted upon by another force, such as friction with the air or another object, gravity, or other external forces present in its environment. These forces will cause the ball to slow down, change direction, or come to a stop depending on their magnitude and direction.
It's important to note that the ball's motion after the string is cut will depend on various factors, including its initial velocity, the angle at which the string is cut, and the presence of other forces in the environment.