BPSC 71st CCE Prelims General Studies · Question 125 of 150

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.

• (a)The principle of conservation of energy is violated — 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)Gravitational force is violated — 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)Gravitational force is not violated — 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.

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.

The reasoning here is not arithmetic; it is knowing which law the phenomenon bears on and refusing to be startled by a half-told story. Move one: read the stem for what it is — a true statement about one form of energy shrinking, presented so that it LOOKS like a contradiction. Move two: ask where that energy went, and answer it quantitatively rather than by assertion, because the equality is exact. A body released from rest and fallen through h has v squared = 2gh, so its kinetic energy is (1/2)m(2gh) = mgh, the very quantity of potential energy surrendered. Not approximately equal, not mostly — identical. Move three: pick the option that speaks to energy, since that is what the stem is about. The single discriminating fact is that conservation is a statement about the TOTAL, never about any one form. No principle of physics says potential energy must stay constant; several say the sum must. Once that is clear, option (a) collapses, because it treats a transfer between accounts as a loss from the bank. Options (c) and (d) fail differently and are worth separating. Option (c) is simply backwards — gravity is not being violated, it is doing the work that drives the whole process. Option (d) is the more dangerous of the two because it sounds unobjectionable, and a candidate under time pressure may tick it as the safe 'nothing is wrong here' answer; it fails because it does not address the puzzle the stem sets up, and because a force is not the kind of thing that gets violated. Finally, the honest boundary condition, which is also the commonest follow-up question: all of this assumes air resistance is neglected. With drag included the falling body's KE + PE does decrease, the missing energy heating the air and the body; a skydiver at terminal velocity has stopped gaining kinetic energy altogether while still losing height, and every joule of potential energy released is going straight to heat and sound.

• For a body released from rest and falling through a height h, v squared = 2gh, so the kinetic energy gained is (1/2)m(2gh) = mgh — exactly the potential energy lost. The equality is not an approximation, and it holds continuously at every point of the fall, not merely at the start and the end.
• Worked illustration with a 1 kg mass dropped from 20 m at g = 10 m/s squared: at the top, PE 200 J and KE 0; at 10 m, PE 100 J and v = 14.1 m/s so KE 100 J; at the ground, PE 0 and v = 20 m/s so KE 200 J. The total is 200 J at every instant.
• Disposing of candidate objections on 31 October 2025, the Bihar Public Service Commission stated that no law of physics is violated in this situation and that the total of the potential and kinetic energies remains the same.
• The principle of conservation of energy — energy can be transformed but neither created nor destroyed — was established in the 1840s through the work of Julius Robert von Mayer (1842), James Prescott Joule (1843-45) and Hermann von Helmholtz (1847); Emmy Noether proved in 1918 that it follows from the invariance of physical law under translation in time.
• Mechanical energy, the sum KE + PE, is conserved only when the forces doing work are conservative, as gravity is. Under air resistance the sum falls and the difference appears as heat: a skydiver at terminal velocity, about 53 m/s in the belly-to-earth posture, gains no further kinetic energy at all even though potential energy is still being released.
• Nothing is destroyed at impact either. The 200 J carried by that 1 kg mass at 20 m/s becomes sound, heat and permanent deformation of the ground — the same conversion that lets a falling hammer drive a nail, and the same one a hydroelectric station harnesses when it turns the potential energy of stored water into electrical energy.

• Watching only one form of energy: the potential energy really does fall, but conservation is a statement about the TOTAL, and the kinetic energy is rising by exactly the same amount at every height
• Choosing the option about gravitational force because it sounds harmless — the stem poses a question about energy, so the responsive answer is the one about the conservation of energy, and a force is not something that can be 'violated'
• Forgetting that only mechanical energy needs the no-air-resistance assumption: with drag, KE + PE does fall, but total energy is still conserved because the shortfall becomes heat

BPSC prints the proposition as a bare statement and offers four completions built on the words 'violated' and 'not violated', so the real task is choosing which law the phenomenon bears on — and, in a translated paper, resisting an option that merely sounds inoffensive. UPSC never uses that frame. It embeds the same potential-to-kinetic exchange inside a physical situation and makes you apply it: in 1997 it asked where in an elliptical orbit Mercury's kinetic energy is greatest, and in 2001 it asked which statements about an oscillating simple pendulum are correct, including that the amplitude decays with time because energy leaks to the air.

• practice — not a real PYQ

  A body of mass 2 kg is dropped from a height of 10 metres. Taking g = 10 m/s squared and neglecting air resistance, its kinetic energy just before it strikes the ground is

  • (a)20 J
  • (b)100 J
  • (c)200 J
  • (d)400 J

  Answer(c) 200 J — the potential energy lost is mgh = 2 × 10 × 10 = 200 J, and with no air resistance all of it appears as kinetic energy; the same figure follows from v squared = 2gh = 200, giving (1/2) × 2 × 200 = 200 J.

• practice — not a real PYQ

  When a body falls freely under gravity, air resistance being neglected, which one of the following remains constant ?

  • (a)Its potential energy
  • (b)Its kinetic energy
  • (c)Its momentum
  • (d)The sum of its potential and kinetic energies

  Answer(d) The sum of its potential and kinetic energies — the potential energy falls and the kinetic energy rises by exactly the same amount, so the mechanical energy is constant. The momentum keeps increasing because gravity is an external force acting on the body.