The potential energy of a freely falling body continuously decreases.

Question

UnlockIAS · Accepted Answer

Correct — B, The principle of conservation of energy is not violated. The stem is printed as a statement rather than a question, and the four options are alternative conclusions to be drawn from it. What the statement describes is entirely true — as a body falls, its height h falls, so its gravitational potential energy mgh falls with it — and the item is testing whether a candidate can see that nothing has gone missing. It has not. Every joule the body loses as potential energy reappears the same instant as kinetic energy, and the two changes are equal not approximately but exactly. The proof is one line. After falling through a height h from rest, the equation v squared = 2gh gives a kinetic energy of (1/2)mv squared = (1/2)m(2gh) = mgh, which is precisely the potential energy given up. Equivalently, by the work-energy theorem the gravitational force mg does positive work mgh on the body during the fall, and work done on a body is the energy delivered to it. Numbers make it concrete. Drop a 1 kg mass from 20 m and take g = 10 m/s squared. At the top the potential energy is mgh = 200 J and the kinetic energy is zero. Halfway down at 10 m the potential energy is 100 J, while v squared = 2 × 10 × 10 = 200, so the kinetic energy is 100 J. At the ground the potential energy is 0, v = 20 m/s, and the kinetic energy is the full 200 J. The total at every one of those instants is 200 J. The Commission itself settled the point when it disposed of candidate objections on 31 October 2025, stating that no law of physics is violated here and that the total of the potential and kinetic energies remains the same. That total, KE plus PE, is the mechanical energy of the body, and it stays constant whenever the only force doing work is a conservative one such as gravity. Two honest riders. First, mechanical energy is conserved only while air resistance is neglected; with drag the sum falls, and what leaves the mechanical account arrives as heat in the body and the surrounding air, so TOTAL energy is still conserved. Second, at impact the kinetic energy does not vanish either — it becomes sound, heat and permanent deformation of the ground, which is exactly how a falling hammer drives a nail.

Why the other options are wrong — (a) The trap the question is built around, and it works by encouraging you to watch one account instead of both. Potential energy really is disappearing, and if that were the whole balance sheet energy would indeed be vanishing. But conservation applies to the TOTAL energy of the system, and the kinetic account is filling at exactly the rate the potential account empties: mgh lost, (1/2)mv squared = mgh gained, at every height.  (c) Flatly wrong, and it inverts the physics. Gravity is not being defied during the fall — gravity is the agent causing it. The force mg acts downward throughout, does positive work mgh on the body, and that work is precisely what appears as kinetic energy. Take gravity away and there is no fall, no loss of potential energy and no question. A force also is not the sort of thing that can be 'violated'; laws are obeyed or broken, forces simply act.  (d) The subtle one, because a hurried candidate reads it as harmless and true — gravity is certainly not being broken — and stops there. It fails as an answer because it is not responsive: the stem raises a puzzle about ENERGY apparently disappearing, so the option that resolves it must be the one about the conservation of energy. It is also loosely framed, since 'gravitational force' names a force and not a law that could be violated in the first place.

Concept: Energy exists in many forms — kinetic, potential, thermal, chemical, electrical, nuclear, radiant — and the principle of conservation of energy states that in an isolated system the total across all forms is constant: energy can be transformed from one form into another but can be neither created nor destroyed. Stated for heat and work it is the first law of thermodynamics, and it was pieced together in the 1840s by Julius Robert von Mayer (1842), James Prescott Joule (1843-45) and Hermann von Helmholtz (1847). Emmy Noether showed in 1918 that it is not an accident of observation at all but a consequence of symmetry — energy is conserved precisely because the laws of physics do not change with time. A falling body is the simplest illustration in the syllabus. Gravitational potential energy near the Earth's surface is U = mgh, the energy a body holds by virtue of its position, measured from whatever reference level you choose; kinetic energy is K = (1/2)mv squared, the energy it holds by virtue of its motion. Their sum is the mechanical energy. Gravity belongs to a special class called conservative forces, for which the work done between two points depends only on those points and not on the path taken, and for which a potential energy can therefore be defined at all. Whenever only conservative forces do work, mechanical energy alone is conserved. Introduce a non-conservative force — friction, air drag, viscosity — and mechanical energy is no longer constant: the shortfall turns into thermal energy, so total energy is still conserved while the sum KE + PE is not. That distinction, mechanical energy against total energy, is where most exam questions on this topic are actually decided.

State PCS 2025 Q125 — Science & Technology PYQ with Answer

State PCS 2025 Q125 — Science & Technology PYQ with Answer