Assistant Provident Fund Commissioner (APFC) 2016 recruitment test, advertisement 170. Transcribed from the Commission's own booklet (series A, B-CRHE-O-PAPA); answer as per the official UPSC final answer key. This question is in Part B. Answer last reviewed 24 August 2026.

In raising an object to a given height by means of an inclined plane, as compared with raising the object vertically, there is a reduction in

(a)Force to be applied
(b)Work required
(c)Distance covered
(d)Friction force

Answer

Why

Correct — A, (a) Force to be applied.

AN INCLINED PLANE IS A SIMPLE MACHINE, AND EVERY SIMPLE MACHINE TRADES FORCE AGAINST DISTANCE. It never creates work. Fix that sentence first and the item answers itself.

TAKE THE TWO WAYS OF RAISING THE SAME LOAD. Let the object weigh W and let the height be h.

STRAIGHT UP — you must pull with a force equal to W, and you must pull it through the distance h. ALONG A SMOOTH RAMP of slant length L that rises to the same height h — the force needed along the surface is only W x h / L, which is W sin(theta), and you must push it through the longer distance L.

Since the ramp is longer than the height it climbs, L is greater than h, so h / L is less than 1 and the force W x h / L is SMALLER than W. That is the whole gain, and it is the reduction the question is asking about. A gentler ramp — larger L for the same h — reduces the force further. This is why a loading ramp, a hill road that climbs in long zigzags, a wheelchair slope and the thread of a screw all exist: each converts a steep lift into a long gentle push.

THE PRICE IS PAID IN DISTANCE, AND THE WORK IS UNCHANGED. Multiply the smaller force by the longer path and the two changes cancel exactly:

work along the ramp = (W x h / L) x L = W x h = work in lifting straight up

So an ideal inclined plane reduces the force to a fraction h / L and lengthens the path by the reciprocal factor L / h. Nothing is saved except effort per instant, which is exactly what a person or a small motor needs.

THE MECHANICAL ADVANTAGE is that same ratio, MA = L / h = 1 / sin(theta). A ramp 5 metres long rising 1 metre gives an advantage of 5: a 500 newton load can be moved with 100 newtons of push, over five times the distance.

The stem's phrase 'as compared with raising the object vertically' is the instruction to compare the two routes on each quantity separately — force, work, distance, friction — and only one of the four goes DOWN.

Why the others are wrong

(b)Work required — This is the option the whole topic exists to refute, and it is the one worth spending time on. WORK IS FORCE MULTIPLIED BY THE DISTANCE MOVED IN THE DIRECTION OF THE FORCE, and a machine that cuts the force must lengthen the distance in exactly the same proportion. On a frictionless ramp the force is W x h / L and the path is L, so the product is W x h — precisely the work of lifting the load straight up through h. Put another way, the work done against gravity depends only on the weight and the CHANGE OF HEIGHT, never on the path taken to get there, because gravity is a conservative force. No arrangement of ramps, levers or pulleys can reduce it. This is often taught as the golden rule of mechanics: what is gained in force is lost in distance. In the real world the ramp is worse, not better — friction along the surface dissipates energy as heat, so the ACTUAL work done on a real inclined plane EXCEEDS W x h, and its efficiency is below one hundred per cent. So work is not reduced under any reading, ideal or real.
(c)Distance covered — Reduced is the wrong direction: the distance is INCREASED, and that increase is the price of the smaller force. The slant length L of a ramp rising to height h satisfies L = h / sin(theta), and since the sine of any angle below ninety degrees is less than one, L is always greater than h. Vertical lifting is the shortest possible route to a given height, which is why it needs the largest force. The gentler the slope, the easier the push and the further the load must travel: halving the required force means doubling the path. A candidate who marks this option has usually reasoned that the ramp 'makes the job shorter', confusing the effort felt at each moment with the length of the journey. The two move in opposite directions here, and keeping them apart is the single idea this question tests.
(d)Friction force — Also the wrong direction, and for a reason worth seeing clearly. Lifting an object vertically on a rope involves NO surface sliding at all, so there is no force of sliding friction to speak of. The moment the load is placed on a ramp it presses on the surface with a normal reaction N = W cos(theta), and dragging it along that surface brings in a friction force f = mu x N opposing the motion. So the inclined plane INTRODUCES friction where the vertical lift had none. That is why a real ramp is less than perfectly efficient and why the push needed is a little more than the ideal W sin(theta) — you must overcome W sin(theta) plus mu W cos(theta). Reducing friction is a separate engineering problem, solved with rollers, wheels, lubricant or a smoother surface, and it is not what the inclined plane itself does.

Concept

THE INCLINED PLANE is one of the classical SIMPLE MACHINES — the small family of devices that change the size or direction of a force without any source of power of their own. The traditional list is the lever, the wheel and axle, the pulley, the inclined plane, the wedge and the screw, and the last two are inclined planes in disguise: a wedge is a moving inclined plane, and a screw is an inclined plane wrapped around a cylinder, its thread being the ramp and its pitch the rise per turn.

WHAT A SIMPLE MACHINE DOES AND DOES NOT DO. It cannot create energy, and it cannot reduce the work to be done. It redistributes the work over a longer path so that the force needed at any instant is smaller. Formally:

MECHANICAL ADVANTAGE (MA) = load / effort — how many times the machine multiplies the force. VELOCITY RATIO (VR) = distance moved by effort / distance moved by load — how much further the effort must travel. EFFICIENCY = useful work out / work in = MA / VR, always less than one for a real machine.

For an ideal inclined plane, MA = VR = L / h = 1 / sin(theta), and the efficiency is one. For a real one, friction makes MA smaller than VR and efficiency less than one, with the lost energy appearing as heat.

THE FORCES ON A BLOCK ON A SLOPE, which is the standard diagram behind every such question. Resolve the weight W along and perpendicular to the surface:

along the surface, pulling the block down the slope: W sin(theta) perpendicular to the surface, pressed into it: W cos(theta), balanced by the normal reaction N friction, opposing relative motion: f = mu x N = mu W cos(theta)

So the push needed to move the block steadily UP a rough incline is W sin(theta) + mu W cos(theta), and the block will slide down of its own accord once tan(theta) exceeds mu — the angle at which that happens is the ANGLE OF REPOSE.

WHY THE WORK CANNOT CHANGE. Gravity is a conservative force: the work done against it between two points depends only on the difference in height, not on the route. Raising a load of weight W through height h always costs W x h of work whether it goes straight up, up a ramp, up a spiral staircase or up a mountain road. Machines choose the route; they do not change the bill.

General science is a small strand on this APFC paper — about five questions — and it is asked at school level, conceptually rather than numerically. This item prints no figure and no numbers at all: it asks only whether the candidate knows which quantity a ramp reduces and which quantities it leaves alone or makes worse.

The habit the question rewards is the one that answers most physics items on these papers: BEFORE CHOOSING, ASK WHAT IS CONSERVED AND WHAT IS MERELY TRADED. Energy and work are conserved quantities and no device rearranges them in your favour; force, speed, distance and time are the things a machine can trade against one another. An option offering a reduction in a conserved quantity is offering something no machine can deliver, and can be set aside without any calculation.

The second habit is to compare the two situations quantity by quantity rather than forming a general impression that the ramp 'makes it easier'. It does make it easier, in the single specific sense of the force required at each moment. On the same comparison the distance goes up, the friction goes up, and the work stays exactly where it was. Three of the four options here are true statements about the ramp with the direction reversed or the quantity swapped, which is how definitional physics items are usually built.

The practical examples are worth carrying because examiners reach for them: the hairpin bends of a ghat road, the ramp used to roll a drum on to a truck, the wheelchair slope required by building rules, the wedge of an axe, and the screw thread that turns a light rotation into a powerful advance.

Key facts

An inclined plane is a simple machine: it reduces the FORCE needed to raise a load, and increases the DISTANCE over which that force must act.
The ideal force along a smooth ramp is W x h / L, that is W sin(theta), where W is the weight, h the height and L the slant length; it is always less than W.
Mechanical advantage of an ideal inclined plane = L / h = 1 / sin(theta) — the gentler the slope, the greater the advantage.
Work is NOT reduced. Force x distance = (W x h / L) x L = W x h, the same as lifting straight up, because gravity is a conservative force and only the change of height matters.
In practice a ramp costs MORE work than a vertical lift, because friction along the surface dissipates energy as heat and efficiency falls below one hundred per cent.
A vertical lift involves no sliding contact; a ramp introduces a normal reaction N = W cos(theta) and a friction force f = mu x N, so friction is increased rather than reduced.
The classical simple machines are the lever, wheel and axle, pulley, inclined plane, wedge and screw; the wedge is a moving inclined plane and the screw is an inclined plane wrapped round a cylinder.
Efficiency = mechanical advantage / velocity ratio, and it is below one for every real machine.
A body begins to slide down a rough incline when tan(theta) exceeds the coefficient of friction; that angle is the angle of repose.

Study next

Levers of the first, second and third order, and the mechanical advantage of each — the other simple machine examiners ask about most.Pulley systems: how a single fixed pulley changes only direction, while a movable pulley or a block and tackle multiplies force.Work, energy and power — the definitions, their SI units (joule and watt) and the work-energy theorem.Conservation of mechanical energy, and what distinguishes a conservative force such as gravity from a dissipative one such as friction.Static and kinetic friction, the coefficient of friction, the angle of repose, and the methods used to reduce friction.Resolving a force into components, which is the single technique behind every inclined-plane problem.Efficiency of machines and where the lost energy goes, which links this topic to heat and to engine performance.

Common traps

Believing a machine reduces the work. It cannot; it reduces the force and lengthens the path by the same factor.
Reading 'easier' as 'shorter'. The ramp is easier at every instant precisely because it is longer.
Forgetting that a real ramp adds friction, so the actual work exceeds the ideal W x h rather than falling below it.
Using W instead of W sin(theta) for the force along the slope, or W instead of W cos(theta) for the normal reaction.
Assuming mechanical advantage and velocity ratio are equal in practice — they are equal only for an ideal, frictionless machine.
Treating the height as the length of the ramp. The rise h and the slant length L are different quantities, and their ratio is the whole answer.

Physics on EPFO papers comes as one-line conceptual questions with four short options and no figure, drawn from school mechanics, waves, heat, light and electricity. The inclined plane, the lever and the pulley recur because they can be asked without any diagram at all. The characteristic option set offers the same quantity in several directions — force, work, distance, friction here — so recognition of the topic is worthless and only the direction of each effect decides the answer. Where a number does appear it is a single substitution into a standard relation, such as the mechanical advantage of a stated ramp. Prepare by being able to state, for every simple machine, exactly which quantity it multiplies, which it divides, and which it leaves untouched.

Related PYQs

EPFO_APFC_2016_Q76

A sinusoidal transverse wave is travelling on a string. Any point on the string moves in

(a) SHM with the same angular frequency as that of the wave
(b) SHM with a different frequency than that of the wave
(c) Uniform circular motion with the same angular speed as that of the wave
(d) Uniform circular motion with a different angular speed than that of the wave

Answer(a) SHM with the same angular frequency as that of the wave

The transverse-wave item on this same paper — the other school-physics question here, and the same test of knowing exactly what a stated physical situation does rather than recognising the topic.

EPFO_APFC_2023_Q52

For an inelastic collision between two objects, which one among the following statements is correct?

(a) The kinetic energy remains conserved, but not the momentum.
(b) The momentum remains conserved, but not the kinetic energy.
(c) Both the kinetic energy and the momentum remain conserved.
(d) Neither the kinetic energy nor the momentum remains conserved.

Answer(b) The momentum remains conserved, but not the kinetic energy.

An inelastic collision, asking which of momentum and kinetic energy stays conserved — the same discipline of separating the quantity that is conserved from the one that is merely traded.

EPFO_APFC_2023_Q53

A train starting from rest with a uniform acceleration attains a speed of 108 km/h in 5 minutes. The distance covered by the train in attaining the speed is

(a) 9000 m
(b) 4500 m
(c) 355 m
(d) 108 m

Answer(b) 4500 m

A train accelerating uniformly to 108 km/h, asking for the distance covered — mechanics asked as a single substitution into a standard relation, the numerical form this strand takes.

Practice

practice — not a real PYQ
A load weighing 200 N is to be raised through a height of 2 metres using a frictionless inclined plane 5 metres long. The minimum force that must be applied along the plane is
- (a)80 N
- (b)100 N
- (c)200 N
- (d)500 N
Answer(a) 80 N — the force along a smooth incline is W x h / L = 200 x 2 / 5 = 80 N. The work is unchanged at 200 x 2 = 400 joules, which is also 80 x 5, so the smaller force is paid for by the longer path.
practice — not a real PYQ
The mechanical advantage of a smooth inclined plane 10 metres long that rises to a height of 2 metres is
- (a)2
- (b)5
- (c)8
- (d)20
Answer(b) 5 — for an ideal inclined plane the mechanical advantage is the slant length divided by the height, 10 / 2 = 5, which is also 1 / sin(theta).

Why