The classification error that costs marks here is treating "conservative" as a property of a situation rather than of a force. Gravity is conservative whether the body is on a smooth table or a rough one. Friction is non-conservative even when the rough patch is so short that the energy loss is negligible. The surface does not decide; the force does.
NCERT Class 11 Physics Chapter 5 (page 78) defines a conservative force by the path-independence test: the work it does between two points depends only on those endpoints, not on the route taken. Equivalently, the work done around any closed loop is zero, and only such a force admits a potential energy function. That last clause is the useful one — gravity and the spring force have potential-energy formulas precisely because they are conservative. Friction has no potential-energy function, and asking for "the potential energy of friction" is a category error.
Page 80 supplies the contrast. Drag a block around a closed rectangular path on a rough floor and return it to its start: gravity has done zero net work (endpoints coincide), while kinetic friction has done negative work on every one of the four legs, because it reverses direction to stay opposite the motion. Friction's total is negative, never zero. That is the signature of a non-conservative force.
This classification is what licenses K_i + U_i = K_f + U_f. Page 81 states the law with an explicit condition: only conservative forces may do work. The frequent formula-misuse is applying it anyway when friction is clearly present — for instance writing mgh = ½mv² for a block sliding down a rough incline. When a non-conservative force acts, retreat to the work-energy theorem, where its (negative) work appears as an explicit term.
Watch-out: a force doing zero work is not thereby conservative. Normal reaction does zero work on a horizontal slide only because it happens to be perpendicular there — that is a geometric accident of one situation, not the path-independence property.
Select an option to see the explanation. Wrong answers show why your choice was tempting — and name the exact trap it exploits.
According to NCERT Class 11 Physics Chapter 5, a force is classified as conservative when the work it does on a body is:
Answer: A. A states the path-independence definition given on page 78 of NCERT Class 11 Physics Chapter 5 — the work depends only on the endpoints.
Why B is wrong: B is wrong because a conservative force does negative work whenever the displacement opposes it — gravity does negative work on a rising ball, and gravity is conservative.
Why C is wrong: C is wrong because that describes the work-energy theorem, which applies to the NET work of all forces, conservative or not; it is not a classification test.
Why D is wrong: D is wrong because constant speed only means the NET work is zero; individual forces, conservative or otherwise, may each be doing non-zero work.
Which property does a non-conservative force lack, according to the treatment in NCERT Class 11 Physics Chapter 5?
Answer: A. A is correct: page 78 of NCERT Class 11 Physics Chapter 5 ties the existence of a potential energy function to path-independence, so a non-conservative force has no such function.
Why B is wrong: B is wrong because non-conservative forces such as kinetic friction do negative work routinely — that is their characteristic behaviour, not something they lack.
Why C is wrong: C is wrong because kinetic friction has a perfectly definite direction at every instant, namely opposite to the relative sliding motion.
Why D is wrong: D is wrong because every force, conservative or not, is a force and is measured in newtons; the classification is about work, not units.
The condition attached to the statement of mechanical-energy conservation on page 81 of NCERT Class 11 Physics Chapter 5 is that:
Answer: C. C is the stated condition on page 81 of NCERT Class 11 Physics Chapter 5: K_i + U_i = K_f + U_f holds when only conservative forces do work.
Why A is wrong: A is wrong because mechanical energy is conserved along curved smooth paths too — a pendulum swing and a projectile arc both qualify.
Why B is wrong: B is wrong because there is no such inequality; a body momentarily at rest at maximum height has zero kinetic energy and mechanical energy is still conserved.
Why D is wrong: D is wrong because momentum conservation is a separate condition (zero net external force) and neither implies nor is implied by mechanical-energy conservation.
A block is pushed once around a closed rectangular path on a rough horizontal floor, returning exactly to its starting point. Over this complete loop, the work done by gravity and the work done by kinetic friction are respectively:
Answer: C. C is correct: gravity is conservative, so its work round a closed loop is zero (page 78, NCERT Class 11 Physics Chapter 5); friction reverses to oppose motion on every leg, so it does negative work on each and cannot cancel.
Why A is wrong: A is wrong because it applies the closed-loop-zero result to friction, which is exactly the property friction does not have — friction's negative contributions accumulate rather than cancel.
Why B is wrong: B is wrong because gravity's work here is zero, not negative: the block starts and ends at the same height, and the floor is horizontal so displacement is always perpendicular to gravity.
Why D is wrong: D is wrong because kinetic friction always opposes the relative motion, so the angle between it and the displacement is 180° on every leg and its work is never positive.
A student argues: 'On this smooth track friction is absent, so here friction is a conservative force.' The flaw in this reasoning is that:
Answer: D. D is correct: the classification on page 78 of NCERT Class 11 Physics Chapter 5 is a path-independence test on the force, so a force that is absent in one set-up is not thereby reclassified.
Why A is wrong: A is wrong because it disputes the idealisation rather than the logic; even granting a perfectly smooth track, the classification of friction as a force would be unchanged.
Why B is wrong: B is wrong because removing friction does nothing to gravity — gravity's path-independence is intrinsic and is not conferred or removed by the surface.
Why C is wrong: C is wrong because no speed threshold appears anywhere in the classification; kinetic friction is non-conservative at every speed.
A block slides from rest down a rough incline through a vertical drop h and a student writes mgh = ½mv² to find the speed at the bottom. The result obtained is:
Answer: D. D is correct: the equation is the mechanical-energy conservation form, whose stated condition on page 81 of NCERT Class 11 Physics Chapter 5 fails when friction does work; friction's negative work makes the true speed smaller.
Why A is wrong: A is wrong because gravity being conservative is not sufficient — the condition is that ONLY conservative forces do work, and kinetic friction on the rough surface also does work here.
Why B is wrong: B is wrong because no angle makes the friction term vanish; steeper inclines change the normal force and hence the friction magnitude, but never remove it.
Why C is wrong: C is wrong because kinetic friction opposes the sliding motion and so does negative work, removing mechanical energy rather than adding it.
A block slides along a horizontal floor. The normal reaction from the floor does zero work on it. Regarding classification, this observation shows that the normal reaction is:
Answer: B. B is correct: the path-independence test on page 78 of NCERT Class 11 Physics Chapter 5 concerns the force's behaviour across paths, whereas the zero here comes from a 90° angle specific to this horizontal geometry.
Why A is wrong: A is wrong because it generalises a single geometric accident into a general property; on a curved or inclined path the normal force's direction relative to displacement changes.
Why C is wrong: C is wrong because 'contact force' is not a classification criterion — the test is path-independence of work, not the mechanism by which the force arises.
Why D is wrong: D is wrong because it compounds the error in A with a further claim; a potential energy function follows only from genuine path-independence, which has not been established here.
A body is moved from point P to point Q by two different routes. Along route 1 the work done by a certain force is +12 J; along route 2 it is +12 J. Along a third route from P to Q the same force does -4 J. What can be concluded?
Answer: B. B is correct: the definition on page 78 of NCERT Class 11 Physics Chapter 5 requires the work to be the same along every path between the endpoints, so one disagreeing route settles it.
Why A is wrong: A is wrong because path-independence is a universal claim over all paths; agreement on a subset of routes is not evidence for it once a counterexample exists.
Why C is wrong: C is wrong because it discards data to protect a conclusion; the third route is given as a measurement, and one genuine disagreement disproves path-independence.
Why D is wrong: D is wrong because the classification test uses the work values between fixed endpoints, which are already supplied; the force's magnitude is not needed.
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Given
A block of mass m = 2.0 kg is dragged once around a closed square path of side L = 3.0 m on a rough horizontal floor, returning to its starting point. The coefficient of kinetic friction is μ_k = 0.20. Take g = 10 m/s² (exact, as specified by the problem).
Required
The total work done by gravity over the closed loop, the total work done by kinetic friction over the closed loop, and what each result says about the classification of that force.
Concept
A conservative force does zero work around any closed path, because its work depends only on the endpoints and here the endpoints coincide (NCERT Class 11 Physics Chapter 5, page 78). A non-conservative force need not give zero; kinetic friction reverses direction on each leg to stay opposite the motion, so its negative contributions accumulate (page 80).
Formula
Work by a force at a fixed angle to displacement: W = F s cos θ.
Friction magnitude on a horizontal surface: f = μ_k N = μ_k m g.
Total path length round the square: d = 4L.
Substitution
Gravity: the floor is horizontal, so the displacement on every leg is perpendicular to the downward weight, giving θ = 90° and W_grav = m g × (4L) × cos 90°.
Friction: f = 0.20 × 2.0 kg × 10 m/s² , and friction is antiparallel to displacement on every leg, so θ = 180° throughout and W_fric = f × (4L) × cos 180°.
Calculation
W_grav = 2.0 × 10 × 12.0 × 0 = 0 Jf = 0.20 × 2.0 × 10 = 4.0 Nd = 4 × 3.0 = 12.0 mW_fric = 4.0 × 12.0 × (−1) = −48 J
The factor 4 in d = 4L is a counting integer (four sides of a square), cos 90° = 0 and cos 180° = −1 are exact values at exact angles, and g = 10 m/s² is exact as specified by the problem. None of these contribute to the significant-figure count, which is therefore governed by the two-significant-figure data (2.0 kg, 3.0 m, 0.20). Hence W_fric = −4.8 × 10¹ J.
Final answer
W_grav = 0 J over the closed loop — consistent with gravity being conservative.W_fric = −4.8 × 10¹ J over the closed loop — non-zero, and negative, confirming that kinetic friction is non-conservative.
Because friction did work here, mechanical energy was not conserved over this journey: 4.8 × 10¹ J left the block's mechanical store as heat, even though the block ended exactly where it began with gravity's ledger balanced at zero.
Common trap
Reporting W_fric = 0 on the grounds that "the block returned to its start." That argument is the closed-loop test, and it is valid only for a conservative force. Applying it to friction is the formula-misuse this topic exists to prevent: it is the same error as writing K_i + U_i = K_f + U_f for a block on a rough incline. Check the classification of each force before invoking any closed-loop or energy-conservation shortcut.
Similar NEET-style question
A particle is carried from point A to point B and back to A along a path lying entirely in a horizontal plane, with a resistive medium present throughout. Which statement is correct?
(a) Both gravity and the resistive force do zero total work.
(b) Gravity does zero total work; the resistive force does negative total work.
(c) Gravity does negative total work; the resistive force does zero total work.
(d) Both do negative total work.
*(Answer: (b) — gravity is conservative and the endpoints coincide; the resistive force opposes motion throughout and its negative work accumulates.)*
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. 78A force is conservative if the work done by it on a particle moving between two points is independent of the path taken (equivalently, the work done on any closed loop is zero). Examples: gravity, spring force, electrostatic force. Non-conservative forces (friction, air drag) do path-dependent work; mechanical energy is not conserved when they act.
-- NCERT Class 11 Physics, Ch. 5, p. 78If only conservative forces do work on a system, the total mechanical energy E = K + U remains constant: K_i + U_i = K_f + U_f. When non-conservative forces do work, the change in mechanical energy equals the work done by those non-conservative forces (typically negative for friction/drag).
-- NCERT Class 11 Physics, Ch. 5, p. 78If only conservative forces do work on a system, the total mechanical energy E = K + U is constant in time.
| Symbol | Quantity | SI Unit |
|---|---|---|
| K_i, K_f | Initial, final kinetic energy | J |
| U_i, U_f | Initial, final potential energy | J |
These are the exact patterns that cause wrong answers in NEET. Each trap includes when it triggers and how to avoid it.
Root cause: formula misuse
Mechanical-energy conservation requires that ONLY conservative forces do work. When friction or drag is present, use the work-energy theorem directly: K_f - K_i = W_conservative + W_non-conservative, where W_non-conservative is typically negative (energy goes to heat).
Distractor sets m*g*h = (1/2)*m*v^2 for a block sliding down a rough incline.
More in Work, Energy and Power: 11 exam traps and mistakes · 9 formulas · 7 question patterns from its other lessons.
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