If we keep a heavy metallic ball on a thin sheet of paper the paper is torn and the ball drops. But according to Newton's third law of motion every action has an EQUAL and opposite reaction. So when the ball applies force on the paper the paper should apply equal amount of force on the ball and the ball should be stable but it falls. Why does this happen?
You have to look at the net forces on the ball and the paper individually, and not just the action-reaction pair.
Gravity exerts a downward force of $mg$ on the ball and the paper momentarily exerts an equal and opposite force of $mg$ on the ball per Newton's third law. The net force on the ball is momentarily zero and the ball is momentarily stable.
But what about the net force on the paper? If the paper is not supported by something beneath it, the only upward force exerted by the paper on the ball in opposition to the downward force of the ball is due to its tensile strength. If that strength isn't sufficient to support the heavy metallic ball, it tears. Once the paper tears and separates there is no upward force on the ball. The net force on the ball is the downward force of gravity and it freely falls.
If instead a ping bong ball were placed on the paper, the tensile strength of the paper would be sufficient to support the ball. Then the net force on both the ball and paper would be zero and the ball would not fall.
Hope this helps.
Downward gravitational force applied on the sheet.Reaction force on the Ball in upward direction.But thin sheet can not sustain such heavy force and breakdown and losses its continuity and comedown by gravity .At that instant Metallic ball only experiences downward gravitational force so it's fall down.