Question

Even though the magnitudes of action force and reaction force are equal and their directions are opposite, their effects do not get cancelled

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Answer 1

Even though the magnitude of action force and reaction force are equal and their direction are opposite their effect do not get cancelled because they ACT ON DIFFERENT BODIES

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Answer 2

According to Newton's Third " Every action has equal and opposite reaction "

Action = - Reaction

But these forces even though they are equal and opposite they don't cancel each other because they don't act on the same object.

"Action and Reaction forces act on two different objects"

For example:

Consider an object placed on the ground.

We have action force  [weight = mg ] is exerted by the block on the ground. and reaction force is normal force exerted by the ground on block..

Hence as they act on different objects. They do not cancel.