Centrifugal Force Dilemma

You do not feel the centrifugal force. What you feel is the centripetal force (which is the contract/friction force that your seat in your car applies to you) pushing you inward.

Try the following Gedankenexperiment: Imagine your car was not turning, but only being accelerated sideways in a straight line. In which direction would the car have to accelerate, to give you the same feeling you have when turning. In which direction is the force on your car going? You will see, that it's the inwards force that you feel when turning, preventing you from following a straight line.

but I can't understand that if it is pseudo force then why we feel something pushing us outwards during a tight turn in vehicle.

What you are feeling is is a result of your inertia, or resistance to a change in the direction or magnitude of your velocity per Newton's first law. In this case, your body's resistance to a change in direction from a straight line to a curved path.

If you were driving at constant speed in a straight line and suddenly accelerated the car, you would feel pushed backward. If you suddenly applied the brakes you would feel pushed forward. In each of these cases the "force" you feel is not the result of something physical acting on your body. Instead it's the result of your being in an accelerating (non-inertial) reference frame.

Also, I am very confused that when we will apply centrifugal force, since centrifugal will cancel centripetal force so how will the object move in circle in absence of radial acceleration? (My understanding)

The centrifugal force only cancels the centripetal force in the rotating (non inertial) reference frame. It is only needed to apply Newton's second law to explain why you are not accelerating radially outward in your reference frame. For example, if you are making a hard turn the centrifugal force acts to push you outwards towards, say, the car door. The friction of your seat, or perhaps the car door itself, acts as the centripetal force stopping your outward motion.

In the inertial (non-accelerating) reference frame of the road, only the centripetal force exists and is responsible for your radial acceleration towards the center of your circular motion.

Hope this helps.

It is not you who is moving outwards and squeezing into the car door. It is the car door which is moving inwards into you.

Your inertia makes your body tend to keep moving straight. Just like when standing in a bus that brakes - you feel pushed forwards, but in fact it is the bus that is being pulled backwards underneath your feet.

When turning, the car door won't allow that your body continues straight. That would break the door. So it pushes you inwards along with it. That is then the centripetal force - it is inwards and there is no other force involved here.

All in all: The "centrifugal force" is merely an illusion. There is no such force. But the centrifugal effect, if we choose to call it that, is very real.