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Centripetal force acts towards the centre and necessary to keep an object in circular motion. But centrifugal force is equal to the magnitude of centripetal force and acts in outwards direction and hence counteracts the centripetal force. Then why is centripetal force required for circular motion?

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Centripetal force is necessary for an object to stay in circular motion because the only thing that the centripetal force is responsible for changing is the direction of the velocity, and not the magnitude. The centripetal force vector points perpendicular to the velocity vector at every instant in the object's circular path. The centrifugal force isn't an actual inertial force, because the object is accelerating it is a force that is apparent because of an accelerated reference frame, similar to how when you turn in a car you feel a "force" on you from your seat trying to push you the opposite direction of the turn. These aren't actual forces that act on the object, so that don't add to get a zero net force like you are describing in your question. So, in short, the reason that centripetal force is necessary for circular motion is because it changes the direction of the velocity so that the object moves in a circle, and the apparent centrifugal force only happens because the object is moving in an accelerated reference frame.

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Centripetal force acts towards the centre and necessary to keep an object in circular motion.

Correct.

But centrifugal force is equal to the magnitude of centripetal force and acts in outwards direction and hence counteracts the centripetal force.

The centrifugal force is an apparent, or fictitious force, that seems to be responsible for the radially outward motion of an object viewed in the non inertial (rotating) frame of reference. But the radial outward motion is not the result of a radially outward force, as explained below, but a consequence of Newton's first law.

Then why is centripetal force required for circular motion?

The short answer is because the centripetal force is the only real force acting on the object. The centrifugal force is not a real force and without a centripetal force an object will move in uniform motion in a straight line as viewed from an inertial (non rotating) reference frame, due to Newton's first law.

Newton’s first law says an object at rest or in uniform motion in a straight line will remain at rest or in uniform motion in a straight line unless acted upon by an external force. Or, to turn it around, if no external force acts on an object that object will either remain at rest or remain in uniform motion in a straight line.

Viewed from an inertial (non rotating) frame of reference the centripetal force is the external force acting on the object towards the center of the circular path, causing the object to move in a circular path instead of a straight line per Newton’s first law. The centripetal force is the ONLY external force acting on the object.

Viewed in the rotating (non inertial) reference frame, without a centripetal force acting on the object there will appear to be a force causing the object to move radially outward. This is the fictitious centrifugal force. It is fictitious because what is actually being observed is not the consequence of a force. What is being observed is the same uniform straight line motion observed in the inertial frame per Newton’s first law, except that it appears to be motion radially outward when viewed from the rotating (non inertial) frame of reference.

Hope this helps

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Centripetal force is the force that is applied by the constraint that is responsible for circular motion. If the "constraint" somehow becomes inefficient at its job at a point (like, if the rope attached to the stone snaps, or a car undergoing a turn skids or there isn't enough friction) the object will continue to move in a straight line, namely the tangent to that point.

This is due to the inertia of the body.

Now addressing your questions,

But centrifugal force is equal to the magnitude of centripetal force and acts in outwards direction and hence counteracts the centripetal force.

The term centrifugal force isn't some real force. It's not a force at all. So it does not counteract the centripetal force because it has no existence.

In fact, it's just a mathematical construct used while working in an accelerating frame to get Newton's $1$st and $2$nd law working but as we're on the ground, we need not invoke any "pseudo force".

Then why is centripetal force required for circular motion?

As I've mentioned before, centripetal force is required to move the object in circles. It always pulls the object towards the center. The reason the object doesn't swirl into the center is because the object has some mass and hence it just tends to continue motion in a straight line. A force has to be applied continuously to get it going in circles.

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  • $\begingroup$ Thank you very much the upvoter, and also the un-downvoter ;) $\endgroup$ – user8718165 Nov 17 at 7:25

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