My question is that why the net force is not zero considering centrifugal force (mv²/r) in outward direction being balanced by centripetal force(=tension=-mv²/r) in inward direction.

To understand why the net force is not zero when considering centrifugal and centripetal forces, we first need to clarify what these forces represent and how they interact in a circular motion scenario. Let's break it down step by step.

Understanding Forces in Circular Motion

When an object moves in a circular path, it experiences two key forces: centripetal force and centrifugal force. The centripetal force is the real force that acts towards the center of the circle, keeping the object in its curved path. This force can be provided by tension, gravity, friction, or any other force that can pull the object inward. On the other hand, centrifugal force is often described as a perceived force that seems to push an object outward when viewed from a rotating reference frame.

Defining Centripetal and Centrifugal Forces

• Centripetal Force: This is the net force required to keep an object moving in a circular path. It is directed towards the center of the circle and is calculated using the formula: F_c = mv²/r, where m is mass, v is velocity, and r is the radius of the circular path.
• Centrifugal Force: This is not a real force but rather a result of inertia. When you are in a rotating frame of reference, you feel as if there is a force pushing you outward. This sensation is due to your body's tendency to move in a straight line while the circular path forces you to change direction.

Analyzing the Forces

In a scenario where an object is tied to a string and swung in a circle, the tension in the string provides the centripetal force necessary to keep the object moving in that circular path. The tension can be expressed as:

Here, the tension (T) acts inward, while the centrifugal force, which you might feel as pushing outward, is a result of your inertia trying to keep the object moving in a straight line. However, this centrifugal force does not actually exist as a physical force acting on the object; it is simply a byproduct of being in a rotating frame.

Why the Net Force is Not Zero

Now, let’s address the core of your question: why the net force is not zero. In a circular motion scenario, the net force is indeed the centripetal force that acts towards the center. The centrifugal force does not counterbalance the centripetal force because it is not a real force acting on the object. Instead, it is a perceived effect due to the object's inertia.

To illustrate this, consider a car turning around a curve. The friction between the tires and the road provides the centripetal force needed to keep the car on its curved path. If the car were to lose traction (like on ice), there would be no centripetal force to keep it turning, and it would continue moving in a straight line due to inertia, which is what you would feel as the centrifugal effect pushing you against the door of the car.

Conclusion

In summary, while it may seem that centrifugal force balances centripetal force, the reality is that centrifugal force is not a true force acting on the object. The net force in circular motion is the centripetal force, which is essential for maintaining that circular path. Understanding this distinction helps clarify why the net force is not zero and how these forces interact in circular motion.