Prove law of conservation of energy
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Law of conservation of energy states that the energy can neither be created nor destroyed but can be transformed from one form to another. Let us now prove that the above law holds good in the case of a freely falling body. Let a body of mass 'm' placed at a height 'h' above the ground, start falling down from rest.
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Conservation of energy can be rigorously proven by Noether's theorem as a consequence of continuous time translation symmetry ; that is, from the fact that the laws of physics do not change over time.
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