explain why the string stretches while the system is rotating?
What system?
How do you expect us to know what you are talking about?
As the system rotates, the mass is moved in a circle which means that there is a net force acting on it and is directed towards the center. That force is provided by the spring which has to be streched in order to provide the force needed.
When a string is attached to a rotating system, such as a spinning wheel or a rotating cylinder, its tension causes it to stretch. This stretching occurs due to the centrifugal force acting on the string.
To understand this concept, we need to consider a fundamental principle of physics: Newton's First Law of Motion, also known as the law of inertia. This law states that an object will remain at rest or continue moving in a straight line at a constant speed unless acted upon by an external force.
In the case of a rotating system, the string connects the rotating object (e.g., the spinner on a wheel or a point on a rotating cylinder) to a fixed point. As the string rotates along with the system, it experiences an inward force called the centripetal force, which keeps it moving in a circular path.
Now, according to Newton's Third Law of Motion, for every action, there is an equal and opposite reaction. This principle applies to the forces acting on the string. The centripetal force acting inward on the string is balanced by an equal and opposite outward force called the centrifugal force.
The centrifugal force causes the string to stretch. When you spin an object, the centrifugal force tries to pull the string outward, creating tension within the string. The tighter the string is pulled, the greater the centrifugal force acting on it.
Therefore, the string stretches while the system is rotating due to the tension generated by the centrifugal force pulling outward. This stretching effect can be observed in various scenarios, such as a yo-yo being thrown, a spinning top, or a spinning washing machine drum.