Ask a repeater "what is the potential energy of a 2 kg book on a 1 m table?" and most answer 20 J without hesitation. The honest answer is: relative to what? Potential energy has no absolute value. It is defined only up to an additive constant, and only differences in it carry physical meaning. Choosing the floor as zero is a convention you adopt, not a result you derive. Measure from the tabletop and the same book has U = 0; measure from the cellar floor three metres below and it has 80 J. Nothing about the book changed.
NCERT Class 11 Physics Chapter 5, page 78, defines potential energy as energy stored by virtue of position or configuration — stored in the sense that a conservative force can give it back as kinetic energy. The defining relation is that the change in potential energy between two points equals the negative of the work done by the conservative force over that path. Because the force is conservative, that work is path-independent, which is exactly what makes a single-valued U(x) definable at all. A non-conservative force has no potential energy function.
Near Earth's surface, where g is effectively uniform, this gives U = mgh (page 78). Here h is a signed height above your chosen reference, not a distance: a body below the reference level has negative U, which is physically fine. The formula fails once the altitude change is large enough that g varies.
Two things to watch in the exam. First, any question offering a bare numerical PE value must have told you the reference level — if it did not, the intended level is almost always the body's lowest position in the problem. Second, energy questions rarely need the absolute U at all; they need ΔU, and there the reference cancels. Pick a level, write it down, and stay with it for the whole problem.
Select an option to see the explanation. Wrong answers show why your choice was tempting — and name the exact trap it exploits.
According to the definition of potential energy in NCERT Class 11 Physics Chapter 5, potential energy is energy possessed by a body by virtue of its:
Answer: C. C is correct. NCERT Class 11 Physics Chapter 5, page 78, defines potential energy as the energy stored by virtue of position or configuration, recoverable as kinetic energy through a conservative force.
Why A is wrong: A is wrong because energy by virtue of speed is kinetic energy, not potential energy; the two are defined separately in the same chapter.
Why B is wrong: B is wrong because a body's potential energy depends on where it is placed relative to a reference, not on its mass in isolation — an identical body at the reference level has zero potential energy.
Why D is wrong: D is wrong because the rate of doing work is power, a different quantity measured in watts rather than joules.
In the expression U = mgh for gravitational potential energy near Earth's surface, the symbol h denotes:
Answer: C. C is correct. In NCERT Class 11 Physics Chapter 5, page 78, h is measured from a freely chosen reference level and carries a sign — a body below that level has negative potential energy.
Why A is wrong: A is wrong because U = mgh depends only on the vertical coordinate of the endpoint, not on the length of the route taken to get there — path-independence is precisely what makes the potential energy function definable.
Why B is wrong: B is wrong because the Earth's radius appears in the general form U = −GMm/r, which is the expression used when the altitude change is large enough that g varies.
Why D is wrong: D is wrong because forcing h to be positive would make it impossible to describe a body below the reference level, whose potential energy is genuinely negative.
For which of the following is a potential energy function definable?
Answer: A. A is correct. A potential energy function exists only for a conservative force, whose work between two points is path-independent; gravity near Earth's surface satisfies this, giving U = mgh (NCERT Class 11 Physics Chapter 5, page 78).
Why B is wrong: B is wrong because the work done against kinetic friction depends on the length of the path taken, so no single-valued function of position can represent it.
Why C is wrong: C is wrong because drag, like friction, dissipates energy along the path and its work is route-dependent, so no potential energy can be assigned.
Why D is wrong: D is wrong because a force that varies with time rather than being a fixed function of position cannot define a potential energy at each point in space.
A body of mass 5.0 kg is raised from the floor of a room to a shelf 2.0 m above it. Taking g = 10 m/s² (exact) and the floor as the reference level, its gravitational potential energy on the shelf is:
Answer: D. D is correct. U = mgh = 5.0 × 10 × 2.0 = 1.0 × 10² J, using the near-Earth form given in NCERT Class 11 Physics Chapter 5, page 78.
Why A is wrong: A is wrong because 10 J = 5.0 × 2.0 is mass times height with g left out; potential energy needs the weight mg, not the mass.
Why B is wrong: B is wrong because it doubles the correct result, as though the height were 4.0 m rather than 2.0 m.
Why C is wrong: C is wrong because it multiplies mass by g and omits the height entirely, giving the body's weight in newtons rather than an energy.
A stone of mass 2.0 kg rests on the floor of a room. The reference level for potential energy is taken at the ceiling, 3.0 m above the floor. Taking g = 10 m/s² (exact), the stone's gravitational potential energy is:
Answer: B. B is correct. The stone lies 3.0 m below the chosen reference, so h = −3.0 m and U = 2.0 × 10 × (−3.0) = −60 J. Negative potential energy is entirely admissible; only differences in U are physically meaningful (NCERT Class 11 Physics Chapter 5, page 78).
Why A is wrong: A is wrong because it confuses potential energy with kinetic energy — a body at rest has zero kinetic energy, but its potential energy depends only on position relative to the reference.
Why C is wrong: C is wrong because it drops the sign of h and treats the 3.0 m as a distance; the stone is below the reference level, not above it.
Why D is wrong: D is wrong because the reference level is a free choice of convention, and placing it at the ceiling is as legitimate as placing it at the floor.
A lift carries a 60 kg passenger from the ground floor to a landing 8.0 m higher, then down to a basement 4.0 m below the ground floor. Taking g = 10 m/s² (exact), the change in the passenger's gravitational potential energy over the whole journey is:
Answer: D. D is correct. Only the endpoints matter: the passenger finishes 4.0 m below the start, so ΔU = mgΔh = 60 × 10 × (−4.0) = −2.4 × 10³ J. This is independent of the reference level chosen, and of the intermediate trip to the landing.
Why A is wrong: A is wrong because it adds the two vertical legs as distances (8.0 + 4.0 = 12 m), treating potential energy change as if it accumulated along the path rather than depending only on the endpoints.
Why B is wrong: B is wrong because it has the right magnitude but the wrong sign: the passenger ends below the starting point, so the potential energy has decreased.
Why C is wrong: C is wrong because it uses only the upward 8.0 m leg and discards the descent into the basement.
A question reads: "A ball of mass 1.0 kg is held at a certain point. Find its gravitational potential energy." No other information is given. The correct response is that the question:
Answer: B. B is correct. Potential energy is defined only up to an additive constant, so a bare numerical value requires a stated reference level; only differences in U are determined by the physics (NCERT Class 11 Physics Chapter 5, page 78).
Why A is wrong: A is wrong because it asserts exactly the misconception this topic targets — U has no absolute value, and the same ball at the same point takes different values under different reference choices.
Why C is wrong: C is wrong because speed determines kinetic energy; the potential energy of the ball is fixed by its position relative to the reference, whatever its speed.
Why D is wrong: D is wrong because the absence of g is a minor gap that a standard value would fill; the fundamental omission is the reference level, without which no number is determined at all.
Two students compute the gravitational potential energy of the same 4.0 kg block sitting on a table 1.5 m above the floor. Student P takes the floor as reference; student Q takes the tabletop as reference. They then each compute the change in potential energy when the block is lifted 0.50 m above the tabletop. Taking g = 10 m/s² (exact), which statement is correct?
Answer: A. A is correct. Student P gets U_i = 4.0 × 10 × 1.5 = 60 J while student Q gets U_i = 0, a difference of 60 J. But both compute ΔU = mgΔh = 4.0 × 10 × 0.50 = 20 J, because the reference constant cancels in any difference (NCERT Class 11 Physics Chapter 5, page 78).
Why B is wrong: B is wrong on the initial values: shifting the reference level by 1.5 m shifts every potential energy value by mg × 1.5 = 60 J, so P and Q cannot agree on U_i.
Why C is wrong: C is wrong on both counts, and reverses the physics: it is the initial values that are convention-dependent and the difference ΔU that is fixed.
Why D is wrong: D is wrong on ΔU: the additive constant that distinguishes the two reference choices subtracts out of any difference, so both students must arrive at the same 20 J.
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Given
A spring-loaded toy of mass 0.20 kg is held at a point 2.5 m above a laboratory bench. The bench top is 0.80 m above the floor. Take g = 10 m/s² (exact).
Required
The toy's gravitational potential energy (a) with the bench top as reference, (b) with the floor as reference; and the change in potential energy when it is lowered to the bench top.
Concept
Gravitational potential energy near Earth's surface is defined relative to a freely chosen reference level. Its absolute value is convention-dependent; only differences between two positions are fixed by the physics. (NCERT Class 11 Physics Chapter 5, page 78.)
Formula
U = mgh, with h the signed height above the reference level. For a change between two positions, ΔU = mg(h_f − h_i).
Substitution
• (a) Reference at bench top: h = +2.5 m, so U_bench = 0.20 × 10 × 2.5.• (b) Reference at floor: the toy is 2.5 + 0.80 = 3.3 m above the floor, so h = +3.3 m and U_floor = 0.20 × 10 × 3.3.• (c) Lowering to the bench top: h_f − h_i = −2.5 m, so ΔU = 0.20 × 10 × (−2.5).
Calculation
• (a) U_bench = 0.20 × 10 × 2.5 = 5.0 J• (b) U_floor = 0.20 × 10 × 3.3 = 6.6 J• (c) ΔU = 0.20 × 10 × (−2.5) = −5.0 J
Here g = 10 m/s² is an exact problem-defined value, as is the factor relating the two reference levels; neither constrains the significant-figure count. The measured quantities (0.20 kg, 2.5 m, 0.80 m) carry two significant figures each, so the answers are quoted to two.
Final answer
With the bench top as reference, U = 5.0 J. With the floor as reference, U = 6.6 J — the same toy at the same point. The change on lowering to the bench top is ΔU = −5.0 J, and this value is identical under either choice of reference.
Common trap
Treating a potential energy value as an absolute property of the body. The two answers 5.0 J and 6.6 J describe one unchanged toy; the 1.6 J gap is nothing but mg × 0.80 m, the offset between the two reference levels. In any question that asks for a bare numerical U, look for the stated reference before computing; if none is stated, the intended level is almost always the lowest position appearing in the problem. Note also that ΔU never depends on this choice — the offset cancels — which is why energy problems can be worked from any reference you like, provided you fix it at the start and do not switch midway.
Similar NEET-style question
A 1.5 kg book lies on a shelf 1.2 m above the floor of a room whose ceiling is 3.0 m above the same floor. Taking g = 10 m/s² (exact), find the book's gravitational potential energy with (i) the floor as reference and (ii) the ceiling as reference, and show that the energy required to raise it a further 0.40 m is the same in both schemes.
Potential energy U(r) is energy possessed by a body by virtue of its position or configuration in a field of conservative force. The defining relation is F(r) = -dU(r)/dr (in 1D); U is defined up to an additive constant fixed by a chosen reference level.
-- NCERT Class 11 Physics, Ch. 5, p. 78For a body of mass m at height h above a chosen reference level (within a region where g is approximately constant): U = m g h. This is the height-dependent gravitational PE near Earth's surface.
-- NCERT Class 11 Physics, Ch. 5, p. 77Potential energy of a body of mass m at height h above the chosen reference level, in a region where g is approximately constant.
| Symbol | Quantity | SI Unit |
|---|---|---|
| U | Gravitational PE | J |
| m | Mass | kg |
| g | Gravitational acceleration | m/s^2 |
| h | Height above reference level | m |
These are the exact patterns that cause wrong answers in NEET. Each trap includes when it triggers and how to avoid it.
Root cause: concept gap
PE is defined up to an additive constant. Only DIFFERENCES in PE have physical meaning (they equal the negative work done by the conservative force between two points). Choosing the ground as zero is a convention, not a derivation.
Distractor offers a numerical PE value where two different reference levels would give different correct numbers.
More in Work, Energy and Power: 11 exam traps and mistakes · 9 formulas · 6 question patterns from its other lessons.
No question in our NEET 2020–2025 set targets this topic directly.
linear scaling
Thinking PE scales as x not x^2
Page numbers are the ones printed in the current NCERT textbook (2023 rationalised edition), unless marked pre-2023. The books are free at ncert.nic.in.
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